Question

Integral well-defined

score 1k · Answer 1 · 2026-04-24 19:51:16

1k

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Integral well-defined

Published on 24 Apr 2026 - 19:51

score 531 · Answer 2 · 2026-04-24 21:31:24

531

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Integral of $f(x)=\begin{cases} \sin(x), & \text{if } \cos(x)\in \mathbb{Q}\\\sin^2(x), & \text{if }\cos(x) \notin \mathbb{Q} \end{cases}$

Published on 24 Apr 2026 - 21:31

score 50 · Answer 3 · 2026-04-24 21:28:34

50

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Dose convergence in measure imply convergence almost every where?

Published on 24 Apr 2026 - 21:28

score 69 · Answer 4 · 2026-04-24 21:23:53

69

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Lebesgue integral/measure issue

Published on 24 Apr 2026 - 21:23

score 427 · Answer 5 · 2026-04-12 06:47:45

427

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About Boole-Bonferroni inequality

Published on 12 Apr 2026 - 6:47

score 185 · Answer 6 · 2026-04-24 21:34:10

185

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Set of discontinuities of bounded function has measure 0.

Published on 24 Apr 2026 - 21:34

score 242 · Answer 7 · 2026-05-01 06:26:53

242

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To check whether a set is measurable.

Published on 01 May 2026 - 6:26

score 194 · Answer 8 · 2026-04-14 19:49:49

194

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Showing continuity from above of Lebesgue-Stieltjes measure

Published on 14 Apr 2026 - 19:49

score 1.3k · Answer 9 · 2026-04-20 12:18:16

1.3k

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Union of one set of outer measure zero and one set of outer measure $\geq 0$ has outer measure zer0.

Published on 20 Apr 2026 - 12:18

score 85 · Answer 10 · 2026-04-24 21:34:11

85

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How bad can be the behavior of Lebesgue integrable functions?

Published on 24 Apr 2026 - 21:34

score 1.2k · Answer 11 · 2026-05-05 09:20:59

1.2k

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Borel vs Lebesgue measure - Cantor set

Published on 05 May 2026 - 9:20

score 325 · Answer 12 · 2026-04-21 02:16:32

325

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Additivity of Outer Measure for Separated Bounded Sets (using definition of an outer measure only)

Published on 21 Apr 2026 - 2:16

score 77 · Answer 13 · 2026-04-28 12:22:29

77

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Do uniformly grey sets of positive density exist?

Published on 28 Apr 2026 - 12:22

score 33 · Answer 14 · 2026-03-18 23:54:07

33

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E measurable then there is $F=\bigcup_{i=1}^NQ_i$ such that $m^*(E\Delta F)<\varepsilon$.

Published on 18 Mar 2026 - 23:54

score 107 · Answer 15 · 2015-10-12 19:56:15

107

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Independent random variables $X_1$, $X_2$, $X_3$, ... defined on $(\Omega, \mathcal{F}, \mathbb{P})$, each normal mean zero, variance $1$.

Published on 12 Oct 2015 - 19:56

List Question

Integral well-defined

Integral of $f(x)=\begin{cases} \sin(x), & \text{if } \cos(x)\in \mathbb{Q}\\\sin^2(x), & \text{if }\cos(x) \notin \mathbb{Q} \end{cases}$

Dose convergence in measure imply convergence almost every where?

Lebesgue integral/measure issue

About Boole-Bonferroni inequality

Set of discontinuities of bounded function has measure 0.

To check whether a set is measurable.

Showing continuity from above of Lebesgue-Stieltjes measure

Union of one set of outer measure zero and one set of outer measure $\geq 0$ has outer measure zer0.

How bad can be the behavior of Lebesgue integrable functions?

Borel vs Lebesgue measure - Cantor set

Additivity of Outer Measure for Separated Bounded Sets (using definition of an outer measure only)

Do uniformly grey sets of positive density exist?

E measurable then there is $F=\bigcup_{i=1}^NQ_i$ such that $m^*(E\Delta F)<\varepsilon$.

Independent random variables $X_1$, $X_2$, $X_3$, ... defined on $(\Omega, \mathcal{F}, \mathbb{P})$, each normal mean zero, variance $1$.

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