Question

Stuck trying to prove inequality for modulus of an integral.

score 37 · Answer 1 · 2026-04-17 09:06:21

37

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Stuck trying to prove inequality for modulus of an integral.

Published on 17 Apr 2026 - 9:06

score 614 · Answer 2 · 2026-04-15 03:55:45

614

Views

Show that if $f(x)\leq g(x)$ for $x\in S$ and $\int_{S}f=\int_{S}g$, then $f$ and $g$ agree except on a set of measure zero.

Published on 15 Apr 2026 - 3:55

score 1.3k · Answer 3 · 2026-04-09 09:13:58

1.3k

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Difference between a Riemann integral and an integral against a measure

Published on 09 Apr 2026 - 9:13

score 205 · Answer 4 · 2026-04-16 04:11:31

205

Views

Show that if $\int_{Q}f$ exists, then $\int_{y\in B}f(x,y)$ exists for $x\in A-D$, where $D$ is a set of measure zero in $\mathbb{R}^k$

Published on 16 Apr 2026 - 4:11

score 103 · Answer 5 · 2026-03-26 12:04:58

103

Views

absolutely continuous measure - probability theory

Published on 26 Mar 2026 - 12:04

score 104 · Answer 6 · 2026-04-12 01:40:28

104

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Could a functional be defined to be with compact support?

Published on 12 Apr 2026 - 1:40

score 220 · Answer 7 · 2026-04-13 04:13:47

220

Views

Can a probability measure be concentrated on a lower-dimensional space?

Published on 13 Apr 2026 - 4:13

score 77 · Answer 8 · 2026-04-16 06:47:45

77

Views

How to generalized a function $f:\mathbb R\to\mathbb R$, $f(x)\neq 0\forall x\in \mathbb R$, $\int_\mathbb R f=1$?

Published on 16 Apr 2026 - 6:47

score 194 · Answer 9 · 2026-04-12 10:27:11

194

Views

Characterization of a positive finite Borel measure on the circle

Published on 12 Apr 2026 - 10:27

score 85 · Answer 10 · 2026-04-16 00:39:32

85

Views

Prove that $\int_E |g|^2 \mathop{d \mu} = 2 \int_0^\infty x \, \mu(|g| > x) \mathop{dx}$

Published on 16 Apr 2026 - 0:39

score 76 · Answer 11 · 2026-04-11 00:19:22

76

Views

expectation of the weighted sum of positive random variables

Published on 11 Apr 2026 - 0:19

score 510 · Answer 12 · 2026-04-11 20:23:18

510

Views

Essential range of a continous function.

Published on 11 Apr 2026 - 20:23

score 24 · Answer 13 · 2026-04-15 10:26:55

24

Views

$|\langle f, \chi _B \rangle | \leq A \mu (B)$ for all $B \in \mathcal B$ implies $f \in L^\infty$

Published on 15 Apr 2026 - 10:26

score 68 · Answer 14 · 2026-04-13 21:14:23

68

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Outer measure induced by a Jump function

Published on 13 Apr 2026 - 21:14

score 48 · Answer 15 · 2026-04-16 15:35:10

48

Views

show that $\int \left(\sum _k |f_{k_{n}}(x)-f(x)|\right)^p \ < \infty$

Published on 16 Apr 2026 - 15:35

List Question

Stuck trying to prove inequality for modulus of an integral.

Show that if $f(x)\leq g(x)$ for $x\in S$ and $\int_{S}f=\int_{S}g$, then $f$ and $g$ agree except on a set of measure zero.

Difference between a Riemann integral and an integral against a measure

Show that if $\int_{Q}f$ exists, then $\int_{y\in B}f(x,y)$ exists for $x\in A-D$, where $D$ is a set of measure zero in $\mathbb{R}^k$

absolutely continuous measure - probability theory

Could a functional be defined to be with compact support?

Can a probability measure be concentrated on a lower-dimensional space?

How to generalized a function $f:\mathbb R\to\mathbb R$, $f(x)\neq 0\forall x\in \mathbb R$, $\int_\mathbb R f=1$?

Characterization of a positive finite Borel measure on the circle

Prove that $\int_E |g|^2 \mathop{d \mu} = 2 \int_0^\infty x \, \mu(|g| > x) \mathop{dx}$

expectation of the weighted sum of positive random variables

Essential range of a continous function.

$|\langle f, \chi _B \rangle | \leq A \mu (B)$ for all $B \in \mathcal B$ implies $f \in L^\infty$

Outer measure induced by a Jump function

show that $\int \left(\sum _k |f_{k_{n}}(x)-f(x)|\right)^p \ < \infty$

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