Question

If $|f(x)|$ is a measurable function defined on a measurable set $E\subset \mathbb{R}^d$, is $f(x)$ also measurable?

score 56 · Answer 1 · 2026-04-18 13:34:04

56

Views

If $|f(x)|$ is a measurable function defined on a measurable set $E\subset \mathbb{R}^d$, is $f(x)$ also measurable?

Published on 18 Apr 2026 - 13:34

score 106 · Answer 2 · 2026-04-16 18:27:57

106

Views

If $z = f(x,y)$ is continuous on $\mathbb{R}^2$, then is $f(g_1(x), g_2(x))$ measurable, where $g_1$ and $g_2$ are measurable?

Published on 16 Apr 2026 - 18:27

score 173 · Answer 3 · 2026-04-14 18:38:37

173

Views

A more advanced proof for showing $\mathbb{E}[X]=\int_{0}^{\infty}\mathbb{P}(X\geq t)dt$

Published on 14 Apr 2026 - 18:38

score 146 · Answer 4 · 2026-04-13 04:11:11

146

Views

Union of elements in a sigma algebra

Published on 13 Apr 2026 - 4:11

score 100 · Answer 5 · 2026-04-15 06:09:53

100

Views

Why is it enough to consider simple functions on open intervals to prove the Riemann-Lebesgue lemma?

Published on 15 Apr 2026 - 6:09

score 50 · Answer 6 · 2026-04-16 06:44:07

50

Views

Show that $\lim_{x \to \infty} x^p\cdot \mu(\{\omega: |f(\omega)| > x\}) = 0.$

Published on 16 Apr 2026 - 6:44

score 60 · Answer 7 · 2026-04-14 09:21:35

60

Views

Prooving independece of random variables defined on Hilbert space

Published on 14 Apr 2026 - 9:21

score 40 · Answer 8 · 2026-04-13 21:28:55

40

Views

This property of of measurable sets and functions.

Published on 13 Apr 2026 - 21:28

score 99 · Answer 9 · 2026-04-16 07:47:34

99

Views

Proving that $\int f=\inf \left\lbrace\int g : g\text{ is a simple function such that } f\le g \right\rbrace $

Published on 16 Apr 2026 - 7:47

score 228 · Answer 10 · 2026-04-12 20:09:23

228

Views

Proving a Borel Measure on the unit circle.

Published on 12 Apr 2026 - 20:09

score 1.2k · Answer 11 · 2026-04-13 01:15:07

1.2k

Views

Can a set of positive measure and its complement both have empty interior?

Published on 13 Apr 2026 - 1:15

score 49 · Answer 12 · 2026-04-11 08:27:36

49

Views

Writing the integral of an indicator function as a surface integral

Published on 11 Apr 2026 - 8:27

score 126 · Answer 13 · 2026-04-11 00:13:23

126

Views

Why is this measure absolutely continuous?

Published on 11 Apr 2026 - 0:13

score 177 · Answer 14 · 2026-04-15 17:09:32

177

Views

Borel $\sigma$-algebra on subset of $\mathbb{R}^n$

Published on 15 Apr 2026 - 17:09

score 2.2k · Answer 15 · 2026-04-12 11:05:43

2.2k

Views

Lebesgue measure of compact and open sets

Published on 12 Apr 2026 - 11:05

List Question

If $|f(x)|$ is a measurable function defined on a measurable set $E\subset \mathbb{R}^d$, is $f(x)$ also measurable?

If $z = f(x,y)$ is continuous on $\mathbb{R}^2$, then is $f(g_1(x), g_2(x))$ measurable, where $g_1$ and $g_2$ are measurable?

A more advanced proof for showing $\mathbb{E}[X]=\int_{0}^{\infty}\mathbb{P}(X\geq t)dt$

Union of elements in a sigma algebra

Why is it enough to consider simple functions on open intervals to prove the Riemann-Lebesgue lemma?

Show that $\lim_{x \to \infty} x^p\cdot \mu(\{\omega: |f(\omega)| > x\}) = 0.$

Prooving independece of random variables defined on Hilbert space

This property of of measurable sets and functions.

Proving that $\int f=\inf \left\lbrace\int g : g\text{ is a simple function such that } f\le g \right\rbrace $

Proving a Borel Measure on the unit circle.

Can a set of positive measure and its complement both have empty interior?

Writing the integral of an indicator function as a surface integral

Why is this measure absolutely continuous?

Borel $\sigma$-algebra on subset of $\mathbb{R}^n$

Lebesgue measure of compact and open sets

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