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Why can this maximization problem attain the value $+infty$?

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1

$begingroup$

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

share|cite|improve this question

asked yesterday

user63841219user63841219

1518

$endgroup$

add a comment | 

1

$begingroup$

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

share|cite|improve this question

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

share|cite|improve this question

asked yesterday

user63841219user63841219

1518

$endgroup$

share|cite|improve this question

asked yesterday

user63841219user63841219

1518

share|cite|improve this question

asked yesterday

user63841219user63841219

1518

asked yesterday

user63841219user63841219

1518

asked yesterday

user63841219user63841219

1518