Question

Prove a function defined by integral is continuous.

score 688 · Answer 1 · 2026-04-09 18:56:45

688

Views

Prove a function defined by integral is continuous.

Published on 09 Apr 2026 - 18:56

score 1.3k · Answer 2 · 2026-04-12 22:58:31

1.3k

Views

Show the set $\{x \in M: f(x)<g(x)\}$ is an open set in metric space when $f,g$ are continuous

Published on 12 Apr 2026 - 22:58

score 873 · Answer 3 · 2026-04-15 03:47:24

873

Views

A martingale bounded from below is $L^1$ bounded

Published on 15 Apr 2026 - 3:47

score 656 · Answer 4 · 2026-04-14 22:07:36

656

Views

Use property to show that if $f_n \rightarrow f$ in measure on finite measure set $E$ then $f_n^2 \rightarrow f^2$ in measure on $E$.

Published on 14 Apr 2026 - 22:07

score 250 · Answer 5 · 2026-04-17 14:00:04

250

Views

For wich $\alpha > 0$ and $\beta \in \mathbb{R}$ is $f: (1,\infty)\to \mathbb{R}: f(x)=\frac{(\ln(x))^\alpha}{(x-1)^\beta}$ Lebesgue integrable?

Published on 17 Apr 2026 - 14:00

score 84 · Answer 6 · 2026-04-17 11:49:34

84

Views

Continuity of a function related to measure theory

Published on 17 Apr 2026 - 11:49

score 152 · Answer 7 · 2026-04-14 12:05:20

152

Views

Proofing that lower bound of two measures exists

Published on 14 Apr 2026 - 12:05

score 225 · Answer 8 · 2026-04-15 04:18:37

225

Views

Outer measure of symmetric difference

Published on 15 Apr 2026 - 4:18

score 79 · Answer 9 · 2026-04-15 15:44:46

79

Views

Find a subset with a specific Lebesgue measure

Published on 15 Apr 2026 - 15:44

score 399 · Answer 10 · 2026-04-16 05:41:55

399

Views

Prove that the measure of the image of G-delta set, $m(f(G))$, is the integral of the derivative, $\int_{G}f^{'} dm$

Published on 16 Apr 2026 - 5:41

score 121 · Answer 11 · 2026-04-12 16:01:12

121

Views

Inner and outer measure

Published on 12 Apr 2026 - 16:01

score 84 · Answer 12 · 2026-04-14 19:45:33

84

Views

Lebesgue integrability of $\frac{f(x)}{x}$

Published on 14 Apr 2026 - 19:45

score 150 · Answer 13 · 2026-04-12 05:36:02

150

Views

Regular tetrahedron/simplex (angle, Lebesgue measure)

Published on 12 Apr 2026 - 5:36

score 74 · Answer 14 · 2026-04-30 11:13:31

74

Views

Existence of unique measure

Published on 30 Apr 2026 - 11:13

score 230 · Answer 15 · 2026-04-09 04:27:47

230

Views

Measurability of piecewise constant function

Published on 09 Apr 2026 - 4:27

List Question

Prove a function defined by integral is continuous.

Show the set $\{x \in M: f(x)<g(x)\}$ is an open set in metric space when $f,g$ are continuous

A martingale bounded from below is $L^1$ bounded

Use property to show that if $f_n \rightarrow f$ in measure on finite measure set $E$ then $f_n^2 \rightarrow f^2$ in measure on $E$.

For wich $\alpha > 0$ and $\beta \in \mathbb{R}$ is $f: (1,\infty)\to \mathbb{R}: f(x)=\frac{(\ln(x))^\alpha}{(x-1)^\beta}$ Lebesgue integrable?

Continuity of a function related to measure theory

Proofing that lower bound of two measures exists

Outer measure of symmetric difference

Find a subset with a specific Lebesgue measure

Prove that the measure of the image of G-delta set, $m(f(G))$, is the integral of the derivative, $\int_{G}f^{'} dm$

Inner and outer measure

Lebesgue integrability of $\frac{f(x)}{x}$

Regular tetrahedron/simplex (angle, Lebesgue measure)

Existence of unique measure

Measurability of piecewise constant function

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