The set $D_v= xin mathbbR^N: D_vf(x) text exists $ is measurable.Compute integral of a Lebesgue measurable setOuter measure proof, assuming measurable set existsShow the existence of a Borel measurable function $phi: mathbbR to mathbbR$is the set measurable?Showing that a set is measurableLet $f : E rightarrow mathbbR$. Show that if $|f|$ is measurable on $E$ and the set $f > 0$ is measurable, then $f$ is measurable on $E$.Give an example of a non-Lebesgue measurable function $f:mathbb R to mathbb R $ such that $|f|$ is a measurable function and …Measurable function constant on uncountable setIs the set $A=xin E$ measurable?Let $f$ be defined on a measurable set $E subset mathbb R^n$. If $a<f<+infty$ and $f=-infty$ are measurable, then $f$ is measurable

What problems would a superhuman have whose skin is constantly hot?

Rationale to prefer local variables over instance variables?

What do you call someone who likes to pick fights?

Is it a Cyclops number? "Nobody" knows!

Are all players supposed to be able to see each others' character sheets?

Did Amazon pay $0 in taxes last year?

Minimizing with differential evolution

Do I really need to have a scientific explanation for my premise?

Drawing close together horizontal lines in Latex

Is there a difference between equilibrium and steady state?

What would be the most expensive material to an intergalactic society?

Signed and unsigned numbers

When a wind turbine does not produce enough electricity how does the power company compensate for the loss?

Why does liquid water form when we exhale on a mirror?

Doesn't allowing a user mode program to access kernel space memory and execute the IN and OUT instructions defeat the purpose of having CPU modes?

Confusion about Complex Continued Fraction

Why does cron require MTA for logging?

Vocabulary for giving just numbers, not a full answer

Can one live in the U.S. and not use a credit card?

Do items de-spawn?

Professor forcing me to attend a conference, I can't afford even with 50% funding

Can I negotiate a patent idea for a raise, under French law?

Specifying a starting column with colortbl package and xcolor

From an axiomatic set theoric approach why can we take uncountable unions?



The set $D_v= xin mathbbR^N: D_vf(x) text exists $ is measurable.


Compute integral of a Lebesgue measurable setOuter measure proof, assuming measurable set existsShow the existence of a Borel measurable function $phi: mathbbR to mathbbR$is the set measurable?Showing that a set is measurableLet $f : E rightarrow mathbbR$. Show that if $|f|$ is measurable on $E$ and the set $f > 0$ is measurable, then $f$ is measurable on $E$.Give an example of a non-Lebesgue measurable function $f:mathbb R to mathbb R $ such that $|f|$ is a measurable function and …Measurable function constant on uncountable setIs the set $A=xin E$ measurable?Let $f$ be defined on a measurable set $E subset mathbb R^n$. If $a<f<+infty$ and $f=-infty$ are measurable, then $f$ is measurable













0












$begingroup$


Let $f:mathbbR^nto mathbbR$ be Lipsticz function. The directional derivative in the direction of $mathbfv$ is given by $$ D_mathbfvf(mathbfx)=lim_tto 0dfracf(mathbfx+tmathbfv)-f(mathbfx)t. $$ Define a set $$ D_mathbfv= mathbfxin mathbbR^n:D_mathbfvf(mathbfx)text exists .$$ Show that $D_mathbfv$ is measurable.



Please help me in proving that.










share|cite|improve this question









$endgroup$











  • $begingroup$
    What have you tried? What do you know? Do you know that $limsup_tto 0 g_t(x)$ of measurable functions for each $t$ is measurable?
    $endgroup$
    – Shashi
    yesterday











  • $begingroup$
    Yes that I know. But how does this help could you please give me some more hint. Then probably I can proceed.
    $endgroup$
    – XYZABC
    yesterday






  • 1




    $begingroup$
    Then the set you are looking for is $x : limsup_tto 0 g_t(x)-liminf_tto 0g_t(x)=0 $ for a suitable chosen $g_t(x)$... Do you get it?
    $endgroup$
    – Shashi
    yesterday










  • $begingroup$
    Okay, I got it. Thanks.
    $endgroup$
    – XYZABC
    yesterday















0












$begingroup$


Let $f:mathbbR^nto mathbbR$ be Lipsticz function. The directional derivative in the direction of $mathbfv$ is given by $$ D_mathbfvf(mathbfx)=lim_tto 0dfracf(mathbfx+tmathbfv)-f(mathbfx)t. $$ Define a set $$ D_mathbfv= mathbfxin mathbbR^n:D_mathbfvf(mathbfx)text exists .$$ Show that $D_mathbfv$ is measurable.



Please help me in proving that.










share|cite|improve this question









$endgroup$











  • $begingroup$
    What have you tried? What do you know? Do you know that $limsup_tto 0 g_t(x)$ of measurable functions for each $t$ is measurable?
    $endgroup$
    – Shashi
    yesterday











  • $begingroup$
    Yes that I know. But how does this help could you please give me some more hint. Then probably I can proceed.
    $endgroup$
    – XYZABC
    yesterday






  • 1




    $begingroup$
    Then the set you are looking for is $x : limsup_tto 0 g_t(x)-liminf_tto 0g_t(x)=0 $ for a suitable chosen $g_t(x)$... Do you get it?
    $endgroup$
    – Shashi
    yesterday










  • $begingroup$
    Okay, I got it. Thanks.
    $endgroup$
    – XYZABC
    yesterday













0












0








0





$begingroup$


Let $f:mathbbR^nto mathbbR$ be Lipsticz function. The directional derivative in the direction of $mathbfv$ is given by $$ D_mathbfvf(mathbfx)=lim_tto 0dfracf(mathbfx+tmathbfv)-f(mathbfx)t. $$ Define a set $$ D_mathbfv= mathbfxin mathbbR^n:D_mathbfvf(mathbfx)text exists .$$ Show that $D_mathbfv$ is measurable.



Please help me in proving that.










share|cite|improve this question









$endgroup$




Let $f:mathbbR^nto mathbbR$ be Lipsticz function. The directional derivative in the direction of $mathbfv$ is given by $$ D_mathbfvf(mathbfx)=lim_tto 0dfracf(mathbfx+tmathbfv)-f(mathbfx)t. $$ Define a set $$ D_mathbfv= mathbfxin mathbbR^n:D_mathbfvf(mathbfx)text exists .$$ Show that $D_mathbfv$ is measurable.



Please help me in proving that.







measure-theory






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked yesterday









XYZABCXYZABC

344110




344110











  • $begingroup$
    What have you tried? What do you know? Do you know that $limsup_tto 0 g_t(x)$ of measurable functions for each $t$ is measurable?
    $endgroup$
    – Shashi
    yesterday











  • $begingroup$
    Yes that I know. But how does this help could you please give me some more hint. Then probably I can proceed.
    $endgroup$
    – XYZABC
    yesterday






  • 1




    $begingroup$
    Then the set you are looking for is $x : limsup_tto 0 g_t(x)-liminf_tto 0g_t(x)=0 $ for a suitable chosen $g_t(x)$... Do you get it?
    $endgroup$
    – Shashi
    yesterday










  • $begingroup$
    Okay, I got it. Thanks.
    $endgroup$
    – XYZABC
    yesterday
















  • $begingroup$
    What have you tried? What do you know? Do you know that $limsup_tto 0 g_t(x)$ of measurable functions for each $t$ is measurable?
    $endgroup$
    – Shashi
    yesterday











  • $begingroup$
    Yes that I know. But how does this help could you please give me some more hint. Then probably I can proceed.
    $endgroup$
    – XYZABC
    yesterday






  • 1




    $begingroup$
    Then the set you are looking for is $x : limsup_tto 0 g_t(x)-liminf_tto 0g_t(x)=0 $ for a suitable chosen $g_t(x)$... Do you get it?
    $endgroup$
    – Shashi
    yesterday










  • $begingroup$
    Okay, I got it. Thanks.
    $endgroup$
    – XYZABC
    yesterday















$begingroup$
What have you tried? What do you know? Do you know that $limsup_tto 0 g_t(x)$ of measurable functions for each $t$ is measurable?
$endgroup$
– Shashi
yesterday





$begingroup$
What have you tried? What do you know? Do you know that $limsup_tto 0 g_t(x)$ of measurable functions for each $t$ is measurable?
$endgroup$
– Shashi
yesterday













$begingroup$
Yes that I know. But how does this help could you please give me some more hint. Then probably I can proceed.
$endgroup$
– XYZABC
yesterday




$begingroup$
Yes that I know. But how does this help could you please give me some more hint. Then probably I can proceed.
$endgroup$
– XYZABC
yesterday




1




1




$begingroup$
Then the set you are looking for is $x : limsup_tto 0 g_t(x)-liminf_tto 0g_t(x)=0 $ for a suitable chosen $g_t(x)$... Do you get it?
$endgroup$
– Shashi
yesterday




$begingroup$
Then the set you are looking for is $x : limsup_tto 0 g_t(x)-liminf_tto 0g_t(x)=0 $ for a suitable chosen $g_t(x)$... Do you get it?
$endgroup$
– Shashi
yesterday












$begingroup$
Okay, I got it. Thanks.
$endgroup$
– XYZABC
yesterday




$begingroup$
Okay, I got it. Thanks.
$endgroup$
– XYZABC
yesterday










0






active

oldest

votes











Your Answer





StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3141082%2fthe-set-d-v-x-in-mathbbrn-d-vfx-text-exists-is-measurable%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























0






active

oldest

votes








0






active

oldest

votes









active

oldest

votes






active

oldest

votes















draft saved

draft discarded
















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3141082%2fthe-set-d-v-x-in-mathbbrn-d-vfx-text-exists-is-measurable%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

How should I support this large drywall patch? Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?How do I cover large gaps in drywall?How do I keep drywall around a patch from crumbling?Can I glue a second layer of drywall?How to patch long strip on drywall?Large drywall patch: how to avoid bulging seams?Drywall Mesh Patch vs. Bulge? To remove or not to remove?How to fix this drywall job?Prep drywall before backsplashWhat's the best way to fix this horrible drywall patch job?Drywall patching using 3M Patch Plus Primer

random experiment with two different functions on unit interval Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Random variable and probability space notionsRandom Walk with EdgesFinding functions where the increase over a random interval is Poisson distributedNumber of days until dayCan an observed event in fact be of zero probability?Unit random processmodels of coins and uniform distributionHow to get the number of successes given $n$ trials , probability $P$ and a random variable $X$Absorbing Markov chain in a computer. Is “almost every” turned into always convergence in computer executions?Stopped random walk is not uniformly integrable

Lowndes Grove History Architecture References Navigation menu32°48′6″N 79°57′58″W / 32.80167°N 79.96611°W / 32.80167; -79.9661132°48′6″N 79°57′58″W / 32.80167°N 79.96611°W / 32.80167; -79.9661178002500"National Register Information System"Historic houses of South Carolina"Lowndes Grove""+32° 48' 6.00", −79° 57' 58.00""Lowndes Grove, Charleston County (260 St. Margaret St., Charleston)""Lowndes Grove"The Charleston ExpositionIt Happened in South Carolina"Lowndes Grove (House), Saint Margaret Street & Sixth Avenue, Charleston, Charleston County, SC(Photographs)"Plantations of the Carolina Low Countrye