Question

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

score 325 · Answer 1 · 2018-10-30 23:24:47

325

Views

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

Published on 30 Oct 2018 - 23:24

score 533 · Answer 2 · 2018-10-31 15:31:54

533

Views

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

Published on 31 Oct 2018 - 15:31

score 51 · Answer 3 · 2018-11-01 00:58:56

51

Views

General techniques for proving a function is Borel measurable

Published on 01 Nov 2018 - 0:58

score 1k · Answer 4 · 2018-11-03 18:24:46

1k

Views

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

Published on 03 Nov 2018 - 18:24

score 33 · Answer 5 · 2018-11-04 11:37:48

33

Views

About a Lebesgue intergrability condition

Published on 04 Nov 2018 - 11:37

score 669 · Answer 6 · 2018-11-04 22:53:38

669

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 04 Nov 2018 - 22:53

score 156 · Answer 7 · 2018-11-04 23:12:26

156

Views

Uncountable family of measurable functions and limits

Published on 04 Nov 2018 - 23:12

score 44 · Answer 8 · 2018-11-05 23:10:01

44

Views

Stochastic Processes ($F_n$ measurable)

Published on 05 Nov 2018 - 23:10

score 77 · Answer 9 · 2018-11-06 01:29:54

77

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 06 Nov 2018 - 1:29

score 2.4k · Answer 10 · 2018-11-06 02:55:15

2.4k

Views

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

Published on 06 Nov 2018 - 2:55

score 109 · Answer 11 · 2018-11-06 02:57:00

109

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 06 Nov 2018 - 2:57

score 45 · Answer 12 · 2026-03-25 03:50:13

45

Views

Is $Tf$ $\mu$- measurable?

Published on 25 Mar 2026 - 3:50

score 191 · Answer 13 · 2018-11-08 15:25:47

191

Views

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

Published on 08 Nov 2018 - 15:25

score 435 · Answer 14 · 2026-03-25 03:00:59

435

Views

A measure for which Lusin's theorem fails?

Published on 25 Mar 2026 - 3:00

score 1.4k · Answer 15 · 2018-11-10 15:09:49

1.4k

Views

Show that Riemann integral and Lebesgue integral coincide.

Published on 10 Nov 2018 - 15:09

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.

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