Why can this maximization problem attain the value $+infty$?As we prove that these two topologies in measures space $mathcalM(mathbbX)$ are really equals?Metrizability of weak convergence by the bounded Lipschitz metricBounded Lipschitz Metric on Space of Positive MeasuresConnection between weak topology in probability and weak* topology in functional analysisRadon measures and Holder distributionsOptimal Transport PDE formulationApplication of Grönwall's inequalityShow that $iint_X times Yvarphi(x)k(x,y)psi(y) d(mu times nu)=int_Y Big[int_Xvarphi(x)k(x,y)dmu Big] psi(y) dnu$Legendre-Fenchel transformation for $varphi, Big(,x, ,, f,big(,Phi,(,x,),big),Big)$.Rudin's RCA; Exercise 3.4 Part (b) Only
Multi tool use
Haman going to the second feast dirty
How can I get players to focus on the story aspect of D&D?
Conservation of Mass and Energy
Windows Server Datacenter Edition - Unlimited Virtual Machines
how to modify custom status text color in UI component grid magento 2?
Is it possible that a question has only two answers?
I can't die. Who am I?
Why aren't there more Gauls like Obelix?
How can I manipulate the output of Information?
Should I take out a loan for a friend to invest on my behalf?
Is divide-by-zero a security vulnerability?
What materials can be used to make a humanoid skin warm?
Does a difference of tense count as a difference of meaning in a minimal pair?
What are some noteworthy "mic-drop" moments in math?
Is it safe to abruptly remove Arduino power?
What would be the most expensive material to an intergalactic society?
School performs periodic password audits. Is my password compromised?
Vocabulary for giving just numbers, not a full answer
Crossing a border with an infant of a different citizenship
Minimizing with differential evolution
Recommendation letter by significant other if you worked with them professionally?
Are small insurances worth it?
What is Earthy controling in the ISS cupola?
How to check whether module is loaded with custom configurations?
Why can this maximization problem attain the value $+infty$?
As we prove that these two topologies in measures space $mathcalM(mathbbX)$ are really equals?Metrizability of weak convergence by the bounded Lipschitz metricBounded Lipschitz Metric on Space of Positive MeasuresConnection between weak topology in probability and weak* topology in functional analysisRadon measures and Holder distributionsOptimal Transport PDE formulationApplication of Grönwall's inequalityShow that $iint_X times Yvarphi(x)k(x,y)psi(y) d(mu times nu)=int_Y Big[int_Xvarphi(x)k(x,y)dmu Big] psi(y) dnu$Legendre-Fenchel transformation for $varphi, Big(,x, ,, f,big(,Phi,(,x,),big),Big)$.Rudin's RCA; Exercise 3.4 Part (b) Only
$begingroup$
Let $X$ and $Y$ be Polish spaces equipped with probability measures $mu$ and $nu$, respectively. Let $gamma$ be a measure on $X times Y$. Consider the maximization problem
$$
sup_varphi,psi Biggint_X varphi , dmu + int_Y psi , dnu - int_X times Y big( varphi(x) + psi(y) big) , dgammaBigg
$$
over all bounded and continuous functions $varphi,psi$.
Why can this maximization problem always attain the value $+infty$ for every initial choices of $mu,nu,gamma$?
real-analysis analysis optimization supremum-and-infimum maxima-minima
asked yesterday
user63841219user63841219
1518
$endgroup$
add a comment |
$begingroup$
Let $X$ and $Y$ be Polish spaces equipped with probability measures $mu$ and $nu$, respectively. Let $gamma$ be a measure on $X times Y$. Consider the maximization problem
$$
sup_varphi,psi Biggint_X varphi , dmu + int_Y psi , dnu - int_X times Y big( varphi(x) + psi(y) big) , dgammaBigg
$$
over all bounded and continuous functions $varphi,psi$.
Why can this maximization problem always attain the value $+infty$ for every initial choices of $mu,nu,gamma$?
real-analysis analysis optimization supremum-and-infimum maxima-minima
asked yesterday
user63841219user63841219
1518
$endgroup$
add a comment |
$begingroup$
Let $X$ and $Y$ be Polish spaces equipped with probability measures $mu$ and $nu$, respectively. Let $gamma$ be a measure on $X times Y$. Consider the maximization problem
$$
sup_varphi,psi Biggint_X varphi , dmu + int_Y psi , dnu - int_X times Y big( varphi(x) + psi(y) big) , dgammaBigg
$$
over all bounded and continuous functions $varphi,psi$.
Why can this maximization problem always attain the value $+infty$ for every initial choices of $mu,nu,gamma$?
real-analysis analysis optimization supremum-and-infimum maxima-minima
asked yesterday
user63841219user63841219
1518
$endgroup$
Let $X$ and $Y$ be Polish spaces equipped with probability measures $mu$ and $nu$, respectively. Let $gamma$ be a measure on $X times Y$. Consider the maximization problem
$$
sup_varphi,psi Biggint_X varphi , dmu + int_Y psi , dnu - int_X times Y big( varphi(x) + psi(y) big) , dgammaBigg
$$
over all bounded and continuous functions $varphi,psi$.
Why can this maximization problem always attain the value $+infty$ for every initial choices of $mu,nu,gamma$?
real-analysis analysis optimization supremum-and-infimum maxima-minima
real-analysis analysis optimization supremum-and-infimum maxima-minima
asked yesterday
user63841219user63841219
1518
asked yesterday
user63841219user63841219
1518
asked yesterday
user63841219user63841219
1518
asked yesterday
user63841219user63841219
1518
asked yesterday
user63841219user63841219
1518
1518
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%2f3141069%2fwhy-can-this-maximization-problem-attain-the-value-infty%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%2f3141069%2fwhy-can-this-maximization-problem-attain-the-value-infty%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
CQ,nKvWBAmF LUF9 O4 wmTAKFgissKFMg7Rx287zDo oyNN76SJH2 0jYkJCaK4,WnfJlTV69Zp,mtm5
