A definition of right-continuous using monotone sequences. The 2019 Stack Overflow Developer Survey Results Are InMonotone convergence theorem of sequences in $mathbbR^n$Real Analysis Monotone Convergence Theorem QuestionLimit of convergent monotone sequenceIs the product of two monotone sequences monotone?Property derived form Monotone Convergence TheoremAlmost sure convergence implies convegence in distribution - proof using monotone convergenceProof verification: $x_n$ is a constant sequence if and only if $x_n$ is both monotone increasing and monotone decreasing.Sequentially continuous for monotone sequences implies sequentially continuous.Proof outline of limit of recursive sequence (using $epsilon-N$ definition)Continuity of functions of monotone sequences
What do these terms in Caesar's Gallic Wars mean?
Deal with toxic manager when you can't quit
Alternative to の
Kerning for subscripts of sigma?
How to type this arrow in math mode?
What is the most efficient way to store a numeric range?
Why can't devices on different VLANs, but on the same subnet, communicate?
Loose spokes after only a few rides
What information about me do stores get via my credit card?
Does adding complexity mean a more secure cipher?
How to notate time signature switching consistently every measure
Can withdrawing asylum be illegal?
Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?
Did the UK government pay "millions and millions of dollars" to try to snag Julian Assange?
Ubuntu Server install with full GUI
Did Scotland spend $250,000 for the slogan "Welcome to Scotland"?
How to type a long/em dash `—`
Likelihood that a superbug or lethal virus could come from a landfill
Why can I use a list index as an indexing variable in a for loop?
The phrase "to the numbers born"?
Short story: child made less intelligent and less attractive
Geography at the pixel level
How can I add encounters in the Lost Mine of Phandelver campaign without giving PCs too much XP?
Short story: man watches girlfriend's spaceship entering a 'black hole' (?) forever
A definition of right-continuous using monotone sequences.
The 2019 Stack Overflow Developer Survey Results Are InMonotone convergence theorem of sequences in $mathbbR^n$Real Analysis Monotone Convergence Theorem QuestionLimit of convergent monotone sequenceIs the product of two monotone sequences monotone?Property derived form Monotone Convergence TheoremAlmost sure convergence implies convegence in distribution - proof using monotone convergenceProof verification: $x_n$ is a constant sequence if and only if $x_n$ is both monotone increasing and monotone decreasing.Sequentially continuous for monotone sequences implies sequentially continuous.Proof outline of limit of recursive sequence (using $epsilon-N$ definition)Continuity of functions of monotone sequences
$begingroup$
The definition of $L = lim_xdownarrow y f(x)$, is that $f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNto y$ with $x_n>y$.
Is there a reference or a proof that this definition is equivalent to that using monotone sequences decreasing to $y$, that is:
$f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNdownarrow y$?
real-analysis probability-theory
asked Mar 24 at 7:36
hfx477346hfx477346
11
$endgroup$
add a comment |
$begingroup$
The definition of $L = lim_xdownarrow y f(x)$, is that $f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNto y$ with $x_n>y$.
Is there a reference or a proof that this definition is equivalent to that using monotone sequences decreasing to $y$, that is:
$f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNdownarrow y$?
real-analysis probability-theory
asked Mar 24 at 7:36
hfx477346hfx477346
11
$endgroup$
add a comment |
$begingroup$
The definition of $L = lim_xdownarrow y f(x)$, is that $f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNto y$ with $x_n>y$.
Is there a reference or a proof that this definition is equivalent to that using monotone sequences decreasing to $y$, that is:
$f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNdownarrow y$?
real-analysis probability-theory
asked Mar 24 at 7:36
hfx477346hfx477346
11
$endgroup$
The definition of $L = lim_xdownarrow y f(x)$, is that $f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNto y$ with $x_n>y$.
Is there a reference or a proof that this definition is equivalent to that using monotone sequences decreasing to $y$, that is:
$f(x_n)to L$ as $ntoinfty$ for all sequences $x_n_ninmathbbNdownarrow y$?
real-analysis probability-theory
real-analysis probability-theory
asked Mar 24 at 7:36
hfx477346hfx477346
11
asked Mar 24 at 7:36
hfx477346hfx477346
11
asked Mar 24 at 7:36
hfx477346hfx477346
11
asked Mar 24 at 7:36
hfx477346hfx477346
11
asked Mar 24 at 7:36
hfx477346hfx477346
11
11
add a comment |
add a comment |
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
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3160245%2fa-definition-of-right-continuous-using-monotone-sequences%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
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.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3160245%2fa-definition-of-right-continuous-using-monotone-sequences%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
