Question

Show that there exists a measurable set $A\in\mathcal{A}$ such that $\chi_{A_n}\to\chi_{A}$ $\mu$-a.e.

score 81 · Answer 1 · 2026-04-15 00:32:33

81

Views

Show that there exists a measurable set $A\in\mathcal{A}$ such that $\chi_{A_n}\to\chi_{A}$ $\mu$-a.e.

Published on 15 Apr 2026 - 0:32

score 75 · Answer 2 · 2026-04-16 18:19:31

75

Views

Why can I not use this alternative, simpler way of showing that $\frac{1}{|a|}f(\frac{x-b}{a})$ is Borel measurable

Published on 16 Apr 2026 - 18:19

score 208 · Answer 3 · 2026-04-12 17:48:26

208

Views

Prove that image of a continuously differential path is a null set

Published on 12 Apr 2026 - 17:48

score 1k · Answer 4 · 2026-04-29 08:29:46

1k

Views

Proof verification: Strong Law of Large Numbers Under Fourth Moment Control

Published on 29 Apr 2026 - 8:29

score 184 · Answer 5 · 2026-04-14 13:53:41

184

Views

Formally proving that the image of $f(E)$ is of measure zero when $E$ is a null set and f is $C^1$

Published on 14 Apr 2026 - 13:53

score 27 · Answer 6 · 2026-04-10 23:03:16

27

Views

Iterated induced outermeasures from premeasure

Published on 10 Apr 2026 - 23:03

score 305 · Answer 7 · 2026-05-14 08:47:22

305

Views

Percolation Textbook Recommendation

Published on 14 May 2026 - 8:47

score 652 · Answer 8 · 2026-05-10 19:15:37

652

Views

Exact value of Hausdorff measure of two dimensional Cantor set

Published on 10 May 2026 - 19:15

score 112 · Answer 9 · 2026-04-10 14:04:29

112

Views

Limits of a multiple integral function

Published on 10 Apr 2026 - 14:04

score 415 · Answer 10 · 2026-04-13 10:47:59

415

Views

function vanishing at infinity and integrability

Published on 13 Apr 2026 - 10:47

score 64 · Answer 11 · 2026-04-15 09:10:18

64

Views

Why is the set $[0\le f_1\le f_2]$ measurable?

Published on 15 Apr 2026 - 9:10

score 319 · Answer 12 · 2026-03-31 12:32:16

319

Views

Measure-theoretic definition of conditional probability

Published on 31 Mar 2026 - 12:32

score 41 · Answer 13 · 2026-04-09 12:13:23

41

Views

Defining powerset of $\Omega = [0, 1]$ in measure theory context

Published on 09 Apr 2026 - 12:13

score 50 · Answer 14 · 2026-05-10 15:26:26

50

Views

Outer approximation of Borel sets by disjoint union of sets of the form $(\frac{k}{n}, \frac{k+1}{n} ]$

Published on 10 May 2026 - 15:26

score 1k · Answer 15 · 2026-04-12 02:43:37

1k

Views

If two functions are equal almost everywhere, the first is continuous a.e., is the second?

Published on 12 Apr 2026 - 2:43

List Question

Show that there exists a measurable set $A\in\mathcal{A}$ such that $\chi_{A_n}\to\chi_{A}$ $\mu$-a.e.

Why can I not use this alternative, simpler way of showing that $\frac{1}{|a|}f(\frac{x-b}{a})$ is Borel measurable

Prove that image of a continuously differential path is a null set

Proof verification: Strong Law of Large Numbers Under Fourth Moment Control

Formally proving that the image of $f(E)$ is of measure zero when $E$ is a null set and f is $C^1$

Iterated induced outermeasures from premeasure

Percolation Textbook Recommendation

Exact value of Hausdorff measure of two dimensional Cantor set

Limits of a multiple integral function

function vanishing at infinity and integrability

Why is the set $[0\le f_1\le f_2]$ measurable?

Measure-theoretic definition of conditional probability

Defining powerset of $\Omega = [0, 1]$ in measure theory context

Outer approximation of Borel sets by disjoint union of sets of the form $(\frac{k}{n}, \frac{k+1}{n} ]$

If two functions are equal almost everywhere, the first is continuous a.e., is the second?

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