Question

A version of fundamental theorem of calculus

score 201 · Answer 1 · 2026-03-25 22:10:57

201

Views

A version of fundamental theorem of calculus

Published on 25 Mar 2026 - 22:10

score 34 · Answer 2 · 2026-04-07 00:03:02

34

Views

$g_n = m(E_n)^{\frac{-1}{q}}\chi_{E_n}$. Show $\int fg_n \rightarrow 0$

Published on 07 Apr 2026 - 0:03

score 97 · Answer 3 · 2020-07-26 19:15:48

97

Views

I'm struggling with a proof that eventually lead to the Jacobi's transformation rule for Lebesgue integrals

Published on 26 Jul 2020 - 19:15

score 143 · Answer 4 · 2020-07-26 21:16:46

143

Views

Lebesgue integral of difference function

Published on 26 Jul 2020 - 21:16

score 746 · Answer 5 · 2020-07-26 21:32:05

746

Views

$\rho(f,g)=\int_E \min(1,|f-g|)dm$. Prove that $f_n$ converges to $f$ in measure if and only if $\rho(f_n,f)\rightarrow 0$ as $n\rightarrow\infty$

Published on 26 Jul 2020 - 21:32

score 46 · Answer 6 · 2020-07-26 23:54:25

46

Views

Show that $\int_0^1\frac{1}{|f(x)-x_0|}dx$ is unbounded

Published on 26 Jul 2020 - 23:54

score 42 · Answer 7 · 2020-07-27 10:18:06

42

Views

What is the condition to split integral in Lebesgue theory?

Published on 27 Jul 2020 - 10:18

score 47 · Answer 8 · 2020-07-27 14:29:43

47

Views

Is it necessarily true that $\int_0^1\frac{1}{(x+f_n(x))\log(n+1)}dx\rightarrow0$ as $n\rightarrow\infty$ under these conditions

Published on 27 Jul 2020 - 14:29

score 927 · Answer 9 · 2026-03-25 17:38:15

927

Views

Understanding reverse Hölder and Minkowski inequalities

Published on 25 Mar 2026 - 17:38

score 88 · Answer 10 · 2020-07-28 00:15:05

88

Views

Prove that $\lim_{j\rightarrow\infty}\int_1^\infty\frac{f_j(x)}{x}dx=\int_1^\infty\frac{f(x)}{x}dx$ under these conditions...

Published on 28 Jul 2020 - 0:15

score 370 · Answer 11 · 2020-07-28 11:14:21

370

Views

Given $f$ is a Lebesgue measurable function and $\int_0^1 x^{2n}f = 0 ~~~ \forall n$ , then show that $f = 0$ a.e.

Published on 28 Jul 2020 - 11:14

score 71 · Answer 12 · 2020-07-28 19:13:38

71

Views

Expected value and Lindeberg condition

Published on 28 Jul 2020 - 19:13

score 52 · Answer 13 · 2020-07-28 22:39:24

52

Views

Show $0<\epsilon<1$ there exists some $\delta_{p,\epsilon}>0$ such that $m(\{x\in X:|f(x)|>\epsilon\})\geq\delta_{p,\epsilon}$ for each $f\in E_p$.

Published on 28 Jul 2020 - 22:39

score 54 · Answer 14 · 2026-03-30 16:02:55

54

Views

Example such that integral w.r.t. absolute continuous measure yields different result

Published on 30 Mar 2026 - 16:02

score 502 · Answer 15 · 2016-07-06 15:16:50

502

Views

An equality concerning the Lebesgue integral

Published on 06 Jul 2016 - 15:16

List Question

A version of fundamental theorem of calculus

$g_n = m(E_n)^{\frac{-1}{q}}\chi_{E_n}$. Show $\int fg_n \rightarrow 0$

I'm struggling with a proof that eventually lead to the Jacobi's transformation rule for Lebesgue integrals

Lebesgue integral of difference function

$\rho(f,g)=\int_E \min(1,|f-g|)dm$. Prove that $f_n$ converges to $f$ in measure if and only if $\rho(f_n,f)\rightarrow 0$ as $n\rightarrow\infty$

Show that $\int_0^1\frac{1}{|f(x)-x_0|}dx$ is unbounded

What is the condition to split integral in Lebesgue theory?

Is it necessarily true that $\int_0^1\frac{1}{(x+f_n(x))\log(n+1)}dx\rightarrow0$ as $n\rightarrow\infty$ under these conditions

Understanding reverse Hölder and Minkowski inequalities

Prove that $\lim_{j\rightarrow\infty}\int_1^\infty\frac{f_j(x)}{x}dx=\int_1^\infty\frac{f(x)}{x}dx$ under these conditions...

Given $f$ is a Lebesgue measurable function and $\int_0^1 x^{2n}f = 0 ~~~ \forall n$ , then show that $f = 0$ a.e.

Expected value and Lindeberg condition

Show $0<\epsilon<1$ there exists some $\delta_{p,\epsilon}>0$ such that $m(\{x\in X:|f(x)|>\epsilon\})\geq\delta_{p,\epsilon}$ for each $f\in E_p$.

Example such that integral w.r.t. absolute continuous measure yields different result

An equality concerning the Lebesgue integral

Trending Questions

Popular # Hahtags

Popular Questions