Question

Generator of a σ-algebra under composition with a measurable function

score 328 · Answer 1 · 2026-04-11 11:18:35

328

Views

Generator of a σ-algebra under composition with a measurable function

Published on 11 Apr 2026 - 11:18

score 536 · Answer 2 · 2026-04-16 10:55:28

536

Views

Prove that left-shift invariant sigma-algebra is contained in the tail sigma-algebra wrt projections

Published on 16 Apr 2026 - 10:55

score 54 · Answer 3 · 2026-04-11 13:04:25

54

Views

General techniques for proving a function is Borel measurable

Published on 11 Apr 2026 - 13:04

score 1k · Answer 4 · 2026-04-14 04:58:34

1k

Views

Constructing a Measure Space where $\mu(A) = 1$ if $A^C$ is Uncountable

Published on 14 Apr 2026 - 4:58

score 36 · Answer 5 · 2026-04-12 00:41:29

36

Views

About a Lebesgue intergrability condition

Published on 12 Apr 2026 - 0:41

score 672 · Answer 6 · 2026-04-15 20:06:40

672

Views

$f:[0,1] \to \mathbb R$ be a differentiable function with bounded derivative, then is $\int_0^1 f'(x)=f(1)-f(0)$?

Published on 15 Apr 2026 - 20:06

score 159 · Answer 7 · 2026-04-12 12:20:10

159

Views

Uncountable family of measurable functions and limits

Published on 12 Apr 2026 - 12:20

score 47 · Answer 8 · 2026-04-17 14:02:10

47

Views

Stochastic Processes ($F_n$ measurable)

Published on 17 Apr 2026 - 14:02

score 80 · Answer 9 · 2026-04-16 10:18:16

80

Views

$X_n$ be a sequence of +ve $L^1$ r.v. converging a.s. to $X\in L^1$ and $E(X_n) \to E(X)$ . Then $E(X_nY)\to E(XY)$ for any bounded r.v. $Y$

Published on 16 Apr 2026 - 10:18

score 2.4k · Answer 10 · 2026-04-14 00:22:40

2.4k

Views

The inverse image of a measurable set under a measurable function is measurable?

Published on 14 Apr 2026 - 0:22

score 112 · Answer 11 · 2026-04-16 06:39:20

112

Views

$X_n$ be a sequence of $L^1$ random variables converging a.s. to $X$ with $\inf_{n\ge 1} E(X_n) >-\infty$. To show $E(|X|)< \infty$

Published on 16 Apr 2026 - 6:39

score 55 · Answer 12 · 2026-05-01 17:36:25

55

Views

Is $Tf$ $\mu$- measurable?

Published on 01 May 2026 - 17:36

score 194 · Answer 13 · 2026-04-15 12:00:01

194

Views

What functions are equal to a measurable function except on a set of measure epsilon?

Published on 15 Apr 2026 - 12:00

score 436 · Answer 14 · 2026-05-10 14:05:45

436

Views

A measure for which Lusin's theorem fails?

Published on 10 May 2026 - 14:05

score 1.4k · Answer 15 · 2026-04-13 22:51:21

1.4k

Views

Show that Riemann integral and Lebesgue integral coincide.

Published on 13 Apr 2026 - 22:51

List Question

Generator of a σ-algebra under composition with a measurable function

Prove that left-shift invariant sigma-algebra is contained in the tail sigma-algebra wrt projections

General techniques for proving a function is Borel measurable

Constructing a Measure Space where $\mu(A) = 1$ if $A^C$ is Uncountable

About a Lebesgue intergrability condition

$f:[0,1] \to \mathbb R$ be a differentiable function with bounded derivative, then is $\int_0^1 f'(x)=f(1)-f(0)$?

Uncountable family of measurable functions and limits

Stochastic Processes ($F_n$ measurable)

$X_n$ be a sequence of +ve $L^1$ r.v. converging a.s. to $X\in L^1$ and $E(X_n) \to E(X)$ . Then $E(X_nY)\to E(XY)$ for any bounded r.v. $Y$

The inverse image of a measurable set under a measurable function is measurable?

$X_n$ be a sequence of $L^1$ random variables converging a.s. to $X$ with $\inf_{n\ge 1} E(X_n) >-\infty$. To show $E(|X|)< \infty$

Is $Tf$ $\mu$- measurable?

What functions are equal to a measurable function except on a set of measure epsilon?

A measure for which Lusin's theorem fails?

Show that Riemann integral and Lebesgue integral coincide.

Trending Questions

Popular # Hahtags

Popular Questions