Question

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

score 458 · Answer 1 · 2026-04-12 23:58:26

458

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Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

Published on 12 Apr 2026 - 23:58

score 81 · Answer 2 · 2026-04-14 04:04:32

81

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Chi function with a set of finite measure

Published on 14 Apr 2026 - 4:04

score 623 · Answer 3 · 2026-04-16 05:14:50

623

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On almost sure convergence of sequence of random variables $\{X_n\}$ such that $\forall p>0, E(|X_n-X|^p)\to 0$ as $n\to \infty$

Published on 16 Apr 2026 - 5:14

score 916 · Answer 4 · 2026-04-14 20:50:10

916

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How to show the parallelogram law holds in $L^p$ (or $l^p$) if and only if $p=2$?

Published on 14 Apr 2026 - 20:50

score 221 · Answer 5 · 2026-04-14 06:03:30

221

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How to prove that Radón-nikodým theorem fails in this case?

Published on 14 Apr 2026 - 6:03

score 114 · Answer 6 · 2026-04-15 09:06:09

114

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Show that $(Meas(X, \Sigma), ||\cdot||_{meas})$ is a Banach space.

Published on 15 Apr 2026 - 9:06

score 193 · Answer 7 · 2026-04-17 09:30:18

193

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A continuous Function from $R$ to a Banach Space is Borel-Measurable

Published on 17 Apr 2026 - 9:30

score 329 · Answer 8 · 2026-04-13 08:57:46

329

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Equivalence of definition of measurable functions.

Published on 13 Apr 2026 - 8:57

score 223 · Answer 9 · 2026-04-15 15:42:16

If $f \in L^p$ with $1 \leq p < \infty$, then for any $\epsilon > 0$ there is a function $g$ with compact support such that $||f-g||_p < \epsilon$

score 1k · Answer 10 · 2026-05-01 01:51:50

1k

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The collection of measurable rectangles form an algebra.

Published on 01 May 2026 - 1:51

score 213 · Answer 11 · 2026-04-11 05:03:28

213

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Premeasures on Algebras

Published on 11 Apr 2026 - 5:03

score 189 · Answer 12 · 2026-04-15 11:20:58

189

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Sigma additivity (disjoint sets)

Published on 15 Apr 2026 - 11:20

score 122 · Answer 13 · 2026-04-14 06:19:38

122

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A property of the Borel measure

Published on 14 Apr 2026 - 6:19

score 106 · Answer 14 · 2026-04-16 22:55:25

106

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Show that $x \mapsto f(x,g(x))$ is Borel measurable.

Published on 16 Apr 2026 - 22:55

score 437 · Answer 15 · 2026-04-17 09:52:30

437

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Proving $\limsup (A_n) \cap \limsup (A^{c}_{n}) = \limsup (A_n \cap A^{c}_{n+1})$

Published on 17 Apr 2026 - 9:52

List Question

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

Chi function with a set of finite measure

On almost sure convergence of sequence of random variables $\{X_n\}$ such that $\forall p>0, E(|X_n-X|^p)\to 0$ as $n\to \infty$

How to show the parallelogram law holds in $L^p$ (or $l^p$) if and only if $p=2$?

How to prove that Radón-nikodým theorem fails in this case?

Show that $(Meas(X, \Sigma), ||\cdot||_{meas})$ is a Banach space.

A continuous Function from $R$ to a Banach Space is Borel-Measurable

Equivalence of definition of measurable functions.

If $f \in L^p$ with $1 \leq p < \infty$, then for any $\epsilon > 0$ there is a function $g$ with compact support such that $||f-g||_p < \epsilon$

The collection of measurable rectangles form an algebra.

Premeasures on Algebras

Sigma additivity (disjoint sets)

A property of the Borel measure

Show that $x \mapsto f(x,g(x))$ is Borel measurable.

Proving $\limsup (A_n) \cap \limsup (A^{c}_{n}) = \limsup (A_n \cap A^{c}_{n+1})$

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