Question

Convolution $f*g(x)$ is continuous if $f \in L^1(\mathbb{R}^n)$ and $g \in L^\infty(\mathbb{R}^n)$

score 746 · Answer 1 · 2026-03-28 21:44:20

746

Views

Convolution $f*g(x)$ is continuous if $f \in L^1(\mathbb{R}^n)$ and $g \in L^\infty(\mathbb{R}^n)$

Published on 28 Mar 2026 - 21:44

score 25 · Answer 2 · 2026-04-03 10:36:43

25

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Find $\int_\mathbb{R} \sum_{n=1}^\infty \frac{1}{3^n} \cdot 1_{[-2^n,2^n]} \, d\lambda$

Published on 03 Apr 2026 - 10:36

score 48 · Answer 3 · 2026-04-03 10:38:34

48

Views

Prove that if $E$ is measurable and $A \subset E$ is measurable, $\gamma$ is simple, then $\int_A \gamma = \int_E \gamma \chi_A $

Published on 03 Apr 2026 - 10:38

score 57 · Answer 4 · 2026-04-11 01:49:16

57

Views

How do I prove that counting measure is subadditive?

Published on 11 Apr 2026 - 1:49

score 78 · Answer 5 · 2019-11-07 20:32:30

78

Views

On the a.e. Convergence of a Measurable Function by Simple Functions of Compact Sets

Published on 07 Nov 2019 - 20:32

score 65 · Answer 6 · 2026-04-09 17:32:10

65

Views

Proof verification: Every null set is a subset of an uncountable null set

Published on 09 Apr 2026 - 17:32

score 1.1k · Answer 7 · 2019-11-08 14:03:02

1.1k

Views

Almost everywhere equal implies measurable

Published on 08 Nov 2019 - 14:03

score 47 · Answer 8 · 2026-04-02 01:56:25

47

Views

Let $A \subseteq \mathbb R$ be an infinite set and for every $x,y \in A, x-y \in \mathbb{Q}$. Now which of following options is true?

Published on 02 Apr 2026 - 1:56

score 143 · Answer 9 · 2026-03-25 16:02:01

143

Views

Proving that $E$ is Lebesgue-measurable $\iff E\cap (n,n+1)$ is Lebesgue-Measurable

Published on 25 Mar 2026 - 16:02

score 89 · Answer 10 · 2019-11-09 14:40:27

89

Views

Given measurable sets $E_k$, find a measurable set $A$ with $0<\mu(E_k\cap A)<\mu(E_k)$

Published on 09 Nov 2019 - 14:40

score 76 · Answer 11 · 2026-03-25 12:48:49

76

Views

Kind of convergence theorem for nets

Published on 25 Mar 2026 - 12:48

score 69 · Answer 12 · 2019-11-09 20:28:15

69

Views

On the a.e. Convergence of a Measurable Function by Simple Functions of Open Sets

Published on 09 Nov 2019 - 20:28

score 13 · Answer 13 · 2026-03-01 08:38:00

13

Views

Property of volume

Published on 01 Mar 2026 - 8:38

score 60 · Answer 14 · 2026-04-10 12:49:44

60

Views

Proof for nullset that does not consist of countable points.

Published on 10 Apr 2026 - 12:49

score 49 · Answer 15 · 2019-11-10 23:29:31

49

Views

For which real numbers $\alpha \in \mathbb{R}$ do the random varibales $Y_{n} = n^{\alpha}X_{n}$ converge to zero in probability and almost surely?

Published on 10 Nov 2019 - 23:29

List Question

Convolution $f*g(x)$ is continuous if $f \in L^1(\mathbb{R}^n)$ and $g \in L^\infty(\mathbb{R}^n)$

Find $\int_\mathbb{R} \sum_{n=1}^\infty \frac{1}{3^n} \cdot 1_{[-2^n,2^n]} \, d\lambda$

Prove that if $E$ is measurable and $A \subset E$ is measurable, $\gamma$ is simple, then $\int_A \gamma = \int_E \gamma \chi_A $

How do I prove that counting measure is subadditive?

On the a.e. Convergence of a Measurable Function by Simple Functions of Compact Sets

Proof verification: Every null set is a subset of an uncountable null set

Almost everywhere equal implies measurable

Let $A \subseteq \mathbb R$ be an infinite set and for every $x,y \in A, x-y \in \mathbb{Q}$. Now which of following options is true?

Proving that $E$ is Lebesgue-measurable $\iff E\cap (n,n+1)$ is Lebesgue-Measurable

Given measurable sets $E_k$, find a measurable set $A$ with $0<\mu(E_k\cap A)<\mu(E_k)$

Kind of convergence theorem for nets

On the a.e. Convergence of a Measurable Function by Simple Functions of Open Sets

Property of volume

Proof for nullset that does not consist of countable points.

For which real numbers $\alpha \in \mathbb{R}$ do the random varibales $Y_{n} = n^{\alpha}X_{n}$ converge to zero in probability and almost surely?

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