Question

Let $\mu$ be a probability measure on $\mathcal{B}(\mathbb{R}^d)$. Find $\int \mu(I_x)dx$

score 43 · Answer 1 · 2018-11-07 02:52:33

43

Views

Let $\mu$ be a probability measure on $\mathcal{B}(\mathbb{R}^d)$. Find $\int \mu(I_x)dx$

Published on 07 Nov 2018 - 2:52

score 176 · Answer 2 · 2026-03-27 13:47:04

176

Views

Counterexample of discontinuous function for integration by parts

Published on 27 Mar 2026 - 13:47

score 135 · Answer 3 · 2018-11-07 19:16:49

135

Views

Integration/measure theory "paradox"?

Published on 07 Nov 2018 - 19:16

score 205 · Answer 4 · 2018-11-07 19:55:55

205

Views

Lebesgue integral of a sequence of floor functions

Published on 07 Nov 2018 - 19:55

score 1.9k · Answer 5 · 2026-03-27 10:10:54

1.9k

Views

A simple function and its canonical form.

Published on 27 Mar 2026 - 10:10

score 184 · Answer 6 · 2018-11-08 09:17:35

184

Views

Integral of positive functions

Published on 08 Nov 2018 - 9:17

score 505 · Answer 7 · 2026-03-25 03:22:11

505

Views

Showing a product of two Lebesgue integrals is $\geq 1$ if the product of the integrands is $\geq 1$

Published on 25 Mar 2026 - 3:22

score 64 · Answer 8 · 2018-11-09 16:54:11

64

Views

How to show that $\int_{(0,1)}\frac{t^{x-1}}{1+t^y}d\lambda(t)=\sum_{n=0}^{\infty}\frac{(-1)^n}{x+ny}$?

Published on 09 Nov 2018 - 16:54

score 143 · Answer 9 · 2018-11-10 10:33:27

143

Views

Convolution in $L^2(-\pi ,\pi )$

Published on 10 Nov 2018 - 10:33

score 1.4k · Answer 10 · 2026-03-25 06:03:50

1.4k

Views

Show that Riemann integral and Lebesgue integral coincide.

Published on 25 Mar 2026 - 6:03

score 44 · Answer 11 · 2026-03-25 19:03:24

44

Views

$f:[a,b] \to \mathbb{R}$ lipschitz continuous $\Leftrightarrow$ $\exists \ g:\|g\|_\infty<+\infty$ so that $f(x)=\int_{[a,x]}g \ d \lambda$

Published on 25 Mar 2026 - 19:03

score 497 · Answer 12 · 2018-11-11 13:12:39

497

Views

Integral over a set of measure 0

Published on 11 Nov 2018 - 13:12

score 295 · Answer 13 · 2018-11-11 15:57:48

295

Views

Integrable if absolutely summable

Published on 11 Nov 2018 - 15:57

score 957 · Answer 14 · 2018-11-11 17:46:59

957

Views

Integral of a product of a ${L^1}_{loc}$ function and a compact support function

Published on 11 Nov 2018 - 17:46

score 193 · Answer 15 · 2018-11-12 02:00:24

193

Views

Prove that $\lim_{n \to \infty} \int_{[0,1]}{x^n}\, dx = 0$. Where $\int$ represents Lebesgue integration.

Published on 12 Nov 2018 - 2:00

List Question

Let $\mu$ be a probability measure on $\mathcal{B}(\mathbb{R}^d)$. Find $\int \mu(I_x)dx$

Counterexample of discontinuous function for integration by parts

Integration/measure theory "paradox"?

Lebesgue integral of a sequence of floor functions

A simple function and its canonical form.

Integral of positive functions

Showing a product of two Lebesgue integrals is $\geq 1$ if the product of the integrands is $\geq 1$

How to show that $\int_{(0,1)}\frac{t^{x-1}}{1+t^y}d\lambda(t)=\sum_{n=0}^{\infty}\frac{(-1)^n}{x+ny}$?

Convolution in $L^2(-\pi ,\pi )$

Show that Riemann integral and Lebesgue integral coincide.

$f:[a,b] \to \mathbb{R}$ lipschitz continuous $\Leftrightarrow$ $\exists \ g:\|g\|_\infty<+\infty$ so that $f(x)=\int_{[a,x]}g \ d \lambda$

Integral over a set of measure 0

Integrable if absolutely summable

Integral of a product of a ${L^1}_{loc}$ function and a compact support function

Prove that $\lim_{n \to \infty} \int_{[0,1]}{x^n}\, dx = 0$. Where $\int$ represents Lebesgue integration.

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