Question

Lebesgue integrability and the divergence of the positive terms

score 425 · Answer 1 · 2026-04-14 16:29:17

425

Views

Lebesgue integrability and the divergence of the positive terms

Published on 14 Apr 2026 - 16:29

score 245 · Answer 2 · 2026-04-16 17:58:16

245

Views

Lebesgue Monotone and Dominated Convergence Theorems

Published on 16 Apr 2026 - 17:58

score 584 · Answer 3 · 2026-04-16 22:53:44

584

Views

Show that $\int_0^1 \frac{x\log x}{(1+x)^2} dx$ is Lebesgue integrable

Published on 16 Apr 2026 - 22:53

score 322 · Answer 4 · 2026-04-11 22:00:48

322

Views

Specific composition of probability kernels yields a probability kernel

Published on 11 Apr 2026 - 22:00

score 2.8k · Answer 5 · 2026-04-14 13:09:26

2.8k

Views

Show that $X = Y$ almost surely

Published on 14 Apr 2026 - 13:09

score 102 · Answer 6 · 2026-04-17 05:19:20

102

Views

Construct a sequence of functions $f_n\in L_1 (\mathbb{R}) \cap L_2 (\mathbb{R})$, $n=1,2,...$ such that $\frac{||f_n||_2}{||f_n||_1} \rightarrow 0$.

Published on 17 Apr 2026 - 5:19

score 225 · Answer 7 · 2026-04-16 13:44:23

225

Views

Show that $\lim\limits_{n \to \infty} \int_{\Bbb R} f(x) g(x+n) dx=0$

Published on 16 Apr 2026 - 13:44

score 48 · Answer 8 · 2026-04-16 15:13:27

48

Views

Proving a pointwise convergent sequence of functions in $L^1$ converges in $L^1$

Published on 16 Apr 2026 - 15:13

score 438 · Answer 9 · 2026-04-10 11:25:07

438

Views

Convergence in measure

Published on 10 Apr 2026 - 11:25

score 1.9k · Answer 10 · 2026-04-12 07:32:40

1.9k

Views

Differentiation inside a conditional expectation

Published on 12 Apr 2026 - 7:32

score 85 · Answer 11 · 2026-04-11 06:19:04

85

Views

Integrability of shifted random variable

Published on 11 Apr 2026 - 6:19

score 101 · Answer 12 · 2026-04-15 16:44:12

101

Views

Lebesgue Outer Measure in R: interval in the cover are limited?

Published on 15 Apr 2026 - 16:44

score 156 · Answer 13 · 2026-04-14 09:07:45

156

Views

Does $0$ belong to the Lebesgue set of Heaviside function?

Published on 14 Apr 2026 - 9:07

score 2.5k · Answer 14 · 2026-04-18 15:17:55

2.5k

Views

Prove that for any $\epsilon >0$ there exists a measurable set $E$ such that $m(E)<\infty$ and $\int_E f>(\int f)-\epsilon$.

Published on 18 Apr 2026 - 15:17

score 543 · Answer 15 · 2026-04-18 15:17:55

543

Views

Suppose $f$ is a non-negative measurable function on $\mathbb{R}$ such that $\int f<\infty$. Is it true that $m(\{x:f(x)=\infty\})=0?$

Published on 18 Apr 2026 - 15:17

List Question

Lebesgue integrability and the divergence of the positive terms

Lebesgue Monotone and Dominated Convergence Theorems

Show that $\int_0^1 \frac{x\log x}{(1+x)^2} dx$ is Lebesgue integrable

Specific composition of probability kernels yields a probability kernel

Show that $X = Y$ almost surely

Construct a sequence of functions $f_n\in L_1 (\mathbb{R}) \cap L_2 (\mathbb{R})$, $n=1,2,...$ such that $\frac{||f_n||_2}{||f_n||_1} \rightarrow 0$.

Show that $\lim\limits_{n \to \infty} \int_{\Bbb R} f(x) g(x+n) dx=0$

Proving a pointwise convergent sequence of functions in $L^1$ converges in $L^1$

Convergence in measure

Differentiation inside a conditional expectation

Integrability of shifted random variable

Lebesgue Outer Measure in R: interval in the cover are limited?

Does $0$ belong to the Lebesgue set of Heaviside function?

Prove that for any $\epsilon >0$ there exists a measurable set $E$ such that $m(E)<\infty$ and $\int_E f>(\int f)-\epsilon$.

Suppose $f$ is a non-negative measurable function on $\mathbb{R}$ such that $\int f<\infty$. Is it true that $m(\{x:f(x)=\infty\})=0?$

Trending Questions

Popular # Hahtags

Popular Questions