Question

Is a density nonnegative almost everywhere?

score 271 · Answer 1 · 2018-09-04 09:38:40

271

Views

Is a density nonnegative almost everywhere?

Published on 04 Sep 2018 - 9:38

score 62 · Answer 2 · 2018-09-04 18:00:07

62

Views

Integration over a strange set w.r.t. Lebesgue measure of $\mathbb{R}^2$

Published on 04 Sep 2018 - 18:00

score 37 · Answer 3 · 2018-09-05 11:57:31

37

Views

Properties of non-negative integrable functions with 1st, 2nd and 3rd powers having same $L^1$-norm

Published on 05 Sep 2018 - 11:57

score 2.9k · Answer 4 · 2018-09-06 10:32:03

2.9k

Views

Proof of Hardy inequality in $\mathbb{R}^n$

Published on 06 Sep 2018 - 10:32

score 132 · Answer 5 · 2018-09-08 04:48:11

132

Views

Divergent Countable Sum from Uncountable Sum

Published on 08 Sep 2018 - 4:48

score 134 · Answer 6 · 2018-09-08 21:26:31

134

Views

Converse of Comparison Theorems for Lebesgue Integrals

Published on 08 Sep 2018 - 21:26

score 2.3k · Answer 7 · 2026-03-25 15:57:31

2.3k

Views

What is a jump function, and which measure does it induce?

Published on 25 Mar 2026 - 15:57

score 42 · Answer 8 · 2018-09-10 17:12:18

42

Views

show that $ f=\lim_{j \to \infty} f_j(x) \ \text{ a.e. everywhere} $

Published on 10 Sep 2018 - 17:12

score 43 · Answer 9 · 2018-09-10 19:02:16

43

Views

If the sections of a function are $\mathscr{L}^2$, would the function be jointly $\mathscr{L}^2$?

Published on 10 Sep 2018 - 19:02

score 84 · Answer 10 · 2018-09-10 22:40:20

84

Views

Show that $ \lim_{a \to \infty} \int_0^\infty f(x-a) \, dx = \int_{-\infty}^\infty f(x) \, dx $ for integrable functions $f \in L^1(\mathbb{R})$

Published on 10 Sep 2018 - 22:40

score 232 · Answer 11 · 2018-09-11 01:25:21

232

Views

Prove that for each $\alpha \in [0,1]$, there exists $E \in M$ with $\mu(E)=\alpha$

Published on 11 Sep 2018 - 1:25

score 263 · Answer 12 · 2018-09-12 06:32:17

263

Views

Egoroff's theorem for non $\sigma$-finite measure spaces, but each $f_n$ is integrable

Published on 12 Sep 2018 - 6:32

score 681 · Answer 13 · 2018-09-12 22:47:36

681

Views

Use Dominated Convergence Theorem to find limit of $\int n f(x) e^{-nx} \, dx$

Published on 12 Sep 2018 - 22:47

score 226 · Answer 14 · 2026-03-26 12:38:25

226

Views

If $\int f(x)dx\leq \liminf\int f_n(x) dx$, then $\lim\limits_{n\to\infty}\int f_n(x)dx=\int \lim\limits_{n\to\infty}f_n(x)dx=\int f(x)dx$

Published on 26 Mar 2026 - 12:38

score 220 · Answer 15 · 2026-03-25 12:53:08

220

Views

How do you compute the following integral $\int\limits_{-\infty}^{+\infty} x^2 e^{-x^2/2} dx$?

Published on 25 Mar 2026 - 12:53

List Question

Is a density nonnegative almost everywhere?

Integration over a strange set w.r.t. Lebesgue measure of $\mathbb{R}^2$

Properties of non-negative integrable functions with 1st, 2nd and 3rd powers having same $L^1$-norm

Proof of Hardy inequality in $\mathbb{R}^n$

Divergent Countable Sum from Uncountable Sum

Converse of Comparison Theorems for Lebesgue Integrals

What is a jump function, and which measure does it induce?

show that $ f=\lim_{j \to \infty} f_j(x) \ \text{ a.e. everywhere} $

If the sections of a function are $\mathscr{L}^2$, would the function be jointly $\mathscr{L}^2$?

Show that $ \lim_{a \to \infty} \int_0^\infty f(x-a) \, dx = \int_{-\infty}^\infty f(x) \, dx $ for integrable functions $f \in L^1(\mathbb{R})$

Prove that for each $\alpha \in [0,1]$, there exists $E \in M$ with $\mu(E)=\alpha$

Egoroff's theorem for non $\sigma$-finite measure spaces, but each $f_n$ is integrable

Use Dominated Convergence Theorem to find limit of $\int n f(x) e^{-nx} \, dx$

If $\int f(x)dx\leq \liminf\int f_n(x) dx$, then $\lim\limits_{n\to\infty}\int f_n(x)dx=\int \lim\limits_{n\to\infty}f_n(x)dx=\int f(x)dx$

How do you compute the following integral $\int\limits_{-\infty}^{+\infty} x^2 e^{-x^2/2} dx$?

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