Question

Convexity of a set defined by integrals of a function on measurable sets

score 29 · Answer 1 · 2026-04-14 09:42:51

29

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Convexity of a set defined by integrals of a function on measurable sets

Published on 14 Apr 2026 - 9:42

score 103 · Answer 2 · 2026-04-16 04:25:34

103

Views

a surjective function is closed iff it maps Borel sets to Borel sets

Published on 16 Apr 2026 - 4:25

score 364 · Answer 3 · 2026-04-14 12:52:40

364

Views

Stein-Shakarchi Real ananlysis problem 2.1: a function has integration 0 in any subset of a given interval.

Published on 14 Apr 2026 - 12:52

score 60 · Answer 4 · 2026-04-12 23:21:20

60

Views

On the measure of a closed subset of a non-measurable set with infinite outer measure

Published on 12 Apr 2026 - 23:21

score 526 · Answer 5 · 2026-03-24 22:10:54

526

Views

Measurability of characteristic function based on measurable function

Published on 24 Mar 2026 - 22:10

score 179 · Answer 6 · 2026-04-11 13:32:53

179

Views

Finite signed measures and their boundedness

Published on 11 Apr 2026 - 13:32

score 156 · Answer 7 · 2026-04-17 07:08:09

156

Views

Finite approximations to transfinite sums of real numbers.

Published on 17 Apr 2026 - 7:08

score 72 · Answer 8 · 2026-04-17 08:50:29

72

Views

$\lim_{N \rightarrow \infty} \int_{\{x \in E : |f_n(x)|>N\}}|f_n(x)|dx = 0.$

Published on 17 Apr 2026 - 8:50

score 159 · Answer 9 · 2026-04-11 18:47:55

159

Views

A counterexample. The pointwise limit of measurable function may not be measurable if the range is not metrizable

Published on 11 Apr 2026 - 18:47

score 90 · Answer 10 · 2026-04-15 10:25:48

90

Views

Theorem 1.40 from Rudin RCA, the last ≤

Published on 15 Apr 2026 - 10:25

score 43 · Answer 11 · 2026-04-09 20:11:37

43

Views

Separating Class Limit

Published on 09 Apr 2026 - 20:11

score 1.6k · Answer 12 · 2026-04-11 06:37:10

1.6k

Views

Borel sigma algebra generated by open intervals proof understanding.

Published on 11 Apr 2026 - 6:37

score 33 · Answer 13 · 2026-04-14 02:36:08

33

Views

Proving that underlying set family is an algebra

Published on 14 Apr 2026 - 2:36

score 111 · Answer 14 · 2026-04-15 06:03:03

111

Views

$F(x):=\int_{[a,x)} f(t) \lambda(dt)$ is absolutely continuous for all $f \in L^1(\lambda)$.

Published on 15 Apr 2026 - 6:03

score 48 · Answer 15 · 2026-04-14 21:53:27

48

Views

Showing $\lim\limits_{R \uparrow \infty} \frac{1}{R^3} \int_{-R}^R \psi^2 (w,x) \, dx = 0$

Published on 14 Apr 2026 - 21:53

List Question

Convexity of a set defined by integrals of a function on measurable sets

a surjective function is closed iff it maps Borel sets to Borel sets

Stein-Shakarchi Real ananlysis problem 2.1: a function has integration 0 in any subset of a given interval.

On the measure of a closed subset of a non-measurable set with infinite outer measure

Measurability of characteristic function based on measurable function

Finite signed measures and their boundedness

Finite approximations to transfinite sums of real numbers.

$\lim_{N \rightarrow \infty} \int_{\{x \in E : |f_n(x)|>N\}}|f_n(x)|dx = 0.$

A counterexample. The pointwise limit of measurable function may not be measurable if the range is not metrizable

Theorem 1.40 from Rudin RCA, the last ≤

Separating Class Limit

Borel sigma algebra generated by open intervals proof understanding.

Proving that underlying set family is an algebra

$F(x):=\int_{[a,x)} f(t) \lambda(dt)$ is absolutely continuous for all $f \in L^1(\lambda)$.

Showing $\lim\limits_{R \uparrow \infty} \frac{1}{R^3} \int_{-R}^R \psi^2 (w,x) \, dx = 0$

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