Question

Measurable sets using closed aproximation

score 54 · Answer 1 · 2026-04-14 07:02:25

54

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Measurable sets using closed aproximation

Published on 14 Apr 2026 - 7:02

score 97 · Answer 2 · 2026-04-14 19:58:54

97

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Weaker condition for determine if a function is measurable.

Published on 14 Apr 2026 - 19:58

score 110 · Answer 3 · 2026-04-13 11:13:25

110

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Show that countable additivity holds(complex measures).

Published on 13 Apr 2026 - 11:13

score 288 · Answer 4 · 2026-04-16 03:42:49

288

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prove that $m(\emptyset) = 0$ where $m$ is countably additive over disjoint collection of sets of $\mathscr{A}$

Published on 16 Apr 2026 - 3:42

score 110 · Answer 5 · 2026-04-24 14:41:55

110

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Assume $b>0$. Show that the Lebesgue integral $\int^{\infty}_{1} x^{-b} e^{b\sin(x)} \sin(2x) dx$ exists iff $b>1$.

Published on 24 Apr 2026 - 14:41

score 81 · Answer 6 · 2026-04-16 08:06:22

Show that $f_n\to f$ in $L^1(\mu)$ iff $\sup\limits_{A \in \mathcal M} \left| \int_{A} f_n d\mu - \int_{A} f d\mu \right| \rightarrow 0$

score 2k · Answer 7 · 2026-04-13 23:30:13

2k

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Jordan measurable sets are Lebesgue measurable

Published on 13 Apr 2026 - 23:30

score 43 · Answer 8 · 2026-04-13 14:09:19

43

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Show $|A \cap B_r(0)^c| \to 0$ for any set $A$ with finite Lebesgue measure

Published on 13 Apr 2026 - 14:09

score 1k · Answer 9 · 2026-04-16 00:19:01

1k

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1. Measurable sets : uncountable union, 2. null set is disjoint from translated rationals

Published on 16 Apr 2026 - 0:19

score 378 · Answer 10 · 2026-04-13 00:27:21

378

Views

Intersection of Borel subset with line

Published on 13 Apr 2026 - 0:27

score 445 · Answer 11 · 2026-04-11 13:18:32

445

Views

Rationale behind construction of measure theory from semirings

Published on 11 Apr 2026 - 13:18

score 342 · Answer 12 · 2026-04-15 03:26:13

342

Views

Covering $\mathbb R$ by translation of a $G_\delta$ set by rationals

Published on 15 Apr 2026 - 3:26

score 243 · Answer 13 · 2026-04-15 00:09:34

243

Views

Does $G_{\delta}+q$ sets cover $\Bbb{R}$ a.e

Published on 15 Apr 2026 - 0:09

score 5k · Answer 14 · 2026-04-17 13:44:27

5k

Views

Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$

Published on 17 Apr 2026 - 13:44

score 193 · Answer 15 · 2026-04-14 03:34:21

193

Views

Outer regularity using countably many open sets

Published on 14 Apr 2026 - 3:34

List Question

Measurable sets using closed aproximation

Weaker condition for determine if a function is measurable.

Show that countable additivity holds(complex measures).

prove that $m(\emptyset) = 0$ where $m$ is countably additive over disjoint collection of sets of $\mathscr{A}$

Assume $b>0$. Show that the Lebesgue integral $\int^{\infty}_{1} x^{-b} e^{b\sin(x)} \sin(2x) dx$ exists iff $b>1$.

Show that $f_n\to f$ in $L^1(\mu)$ iff $\sup\limits_{A \in \mathcal M} \left| \int_{A} f_n d\mu - \int_{A} f d\mu \right| \rightarrow 0$

Jordan measurable sets are Lebesgue measurable

Show $|A \cap B_r(0)^c| \to 0$ for any set $A$ with finite Lebesgue measure

1. Measurable sets : uncountable union, 2. null set is disjoint from translated rationals

Intersection of Borel subset with line

Rationale behind construction of measure theory from semirings

Covering $\mathbb R$ by translation of a $G_\delta$ set by rationals

Does $G_{\delta}+q$ sets cover $\Bbb{R}$ a.e

Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$

Outer regularity using countably many open sets

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