Question

Prove that $\inf\left\{\int_E f d\mu : E \in \mathcal{M}, \mu(E)\geq 0 \right\}>0$

score 96 · Answer 1 · 2026-04-15 02:43:10

96

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Prove that $\inf\left\{\int_E f d\mu : E \in \mathcal{M}, \mu(E)\geq 0 \right\}>0$

Published on 15 Apr 2026 - 2:43

score 97 · Answer 2 · 2026-04-10 10:57:53

97

Views

Help proving a measure is not Borel regular.

Published on 10 Apr 2026 - 10:57

score 380 · Answer 3 · 2026-04-17 04:26:28

380

Views

product of two measurable spaces

Published on 17 Apr 2026 - 4:26

score 873 · Answer 4 · 2026-04-14 05:13:04

873

Views

The canonical form of a simple function (proof verification)

Published on 14 Apr 2026 - 5:13

score 1k · Answer 5 · 2026-04-16 01:03:01

1k

Views

Show an infinite sigma algebra contains an infinite sequence of disjoint sets proof clarification

Published on 16 Apr 2026 - 1:03

score 82 · Answer 6 · 2026-04-11 17:11:06

82

Views

Convergence of measure

Published on 11 Apr 2026 - 17:11

score 313 · Answer 7 · 2026-04-16 10:23:12

313

Views

Show that if $X$ and $Y$ are independent then $E_X(g(X,Y))=E(g(X,Y)|Y).$

Published on 16 Apr 2026 - 10:23

score 150 · Answer 8 · 2026-04-13 19:52:09

Does the intersection of an infinite $\sigma$-algebra with the complement of an element in the $\sigma$-algebra create a new $\sigma$-algebra?

score 354 · Answer 9 · 2026-04-29 12:44:11

354

Views

Pushforward-change-of-variable with quantile function

Published on 29 Apr 2026 - 12:44

score 82 · Answer 10 · 2026-04-13 04:34:01

82

Views

Hint on Cohn, Section 1.3, Problem 8 (Measure Theory)

Published on 13 Apr 2026 - 4:34

score 42 · Answer 11 · 2026-04-14 10:43:08

42

Views

Example of closed strict subspace of $L^p$ that is dense in $L^r$ for $r<p$

Published on 14 Apr 2026 - 10:43

score 69 · Answer 12 · 2026-04-16 11:25:25

69

Views

Why $|y|=|x||T^{-1}\rho(x)|<\varepsilon_k\delta_k$ where $2\delta_k \sup_{0\leq |x|\leq \varepsilon_k}|T^{-1}\rho(x)|$

Published on 16 Apr 2026 - 11:25

score 453 · Answer 13 · 2026-04-12 04:08:54

453

Views

Measurability of an uncountable union

Published on 12 Apr 2026 - 4:08

score 49 · Answer 14 · 2026-04-14 05:49:03

49

Views

Why does there exist such dense set?

Published on 14 Apr 2026 - 5:49

score 1.2k · Answer 15 · 2026-04-16 13:58:43

1.2k

Views

Portmanteau Theorem in Weak Convergence ( Lipschitz functions and lim sup / lim inf )

Published on 16 Apr 2026 - 13:58

List Question

Prove that $\inf\left\{\int_E f d\mu : E \in \mathcal{M}, \mu(E)\geq 0 \right\}>0$

Help proving a measure is not Borel regular.

product of two measurable spaces

The canonical form of a simple function (proof verification)

Show an infinite sigma algebra contains an infinite sequence of disjoint sets proof clarification

Convergence of measure

Show that if $X$ and $Y$ are independent then $E_X(g(X,Y))=E(g(X,Y)|Y).$

Does the intersection of an infinite $\sigma$-algebra with the complement of an element in the $\sigma$-algebra create a new $\sigma$-algebra?

Pushforward-change-of-variable with quantile function

Hint on Cohn, Section 1.3, Problem 8 (Measure Theory)

Example of closed strict subspace of $L^p$ that is dense in $L^r$ for $r<p$

Why $|y|=|x||T^{-1}\rho(x)|<\varepsilon_k\delta_k$ where $2\delta_k \sup_{0\leq |x|\leq \varepsilon_k}|T^{-1}\rho(x)|$

Measurability of an uncountable union

Why does there exist such dense set?

Portmanteau Theorem in Weak Convergence ( Lipschitz functions and lim sup / lim inf )

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