Question

Limit of $\int_E f(nx) dx$ for a $1$-periodic function $f$ on $[0,2\pi]$

score 864 · Answer 1 · 2026-04-14 21:07:11

864

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Limit of $\int_E f(nx) dx$ for a $1$-periodic function $f$ on $[0,2\pi]$

Published on 14 Apr 2026 - 21:07

score 274 · Answer 2 · 2026-04-03 19:57:01

274

Views

Prove that $\|f\|_p \leq \liminf \|f_n\|_p$ under weak convergence

Published on 03 Apr 2026 - 19:57

score 67 · Answer 3 · 2026-04-16 00:44:56

67

Views

For a Lebesgue integrable function $f$, the map $t\mapsto\int \chi_{A+t}f(x) dx $ is continuous

Published on 16 Apr 2026 - 0:44

score 66 · Answer 4 · 2026-03-28 09:53:28

66

Views

If $f ∈ L^1((0, 1))$ is non-negative and $\int_0^1 f=1$, then $\int_0^1 f^{-1}\ge 1$

Published on 28 Mar 2026 - 9:53

score 48 · Answer 5 · 2026-04-14 03:50:24

48

Views

Integration w.r.t nondegenerate Gaussian probability measure on $X$ with mean $0$

Published on 14 Apr 2026 - 3:50

score 78 · Answer 6 · 2026-04-11 05:32:42

78

Views

Lebesgue-integrable function particular characteristic

Published on 11 Apr 2026 - 5:32

score 328 · Answer 7 · 2026-04-12 08:40:14

328

Views

Integral equal $0$ for all $x$ implies $f=0$ a.e.

Published on 12 Apr 2026 - 8:40

score 290 · Answer 8 · 2026-04-19 12:14:01

290

Views

Prove an equality ($L^P$ spaces)

Published on 19 Apr 2026 - 12:14

score 114 · Answer 9 · 2026-04-17 07:59:56

114

Views

For which $\alpha, \beta \in \mathbb{R}$ is $\frac{1}{x^\alpha (\log(x))^\beta} \in L^p((1,\infty)$ where $1\leq p \leq \infty$

Published on 17 Apr 2026 - 7:59

score 80 · Answer 10 · 2026-04-19 17:06:57

80

Views

Hint for Lebesgue theory/functional analysis type of problem

Published on 19 Apr 2026 - 17:06

score 46 · Answer 11 · 2026-04-18 11:57:29

46

Views

Evaluate Integral of $\int_0^{\frac{\pi 2^n}{2}}\sin^{2+d}(u)\prod_{i=1}^{n}\cos^{2-d}(u/2^i)du$

Published on 18 Apr 2026 - 11:57

score 41 · Answer 12 · 2026-04-09 13:38:30

41

Views

Find a function $b$ such that the operator $\frac{d}{dx}+b(x)$ is symmetric with the weight $x^2$

Published on 09 Apr 2026 - 13:38

score 167 · Answer 13 · 2026-04-11 07:31:48

167

Views

Attempting to use dominated convergence theorem

Published on 11 Apr 2026 - 7:31

score 263 · Answer 14 · 2026-04-10 06:18:12

263

Views

Question about inequality relating infinity norm and Lebesgue integral

Published on 10 Apr 2026 - 6:18

score 222 · Answer 15 · 2026-04-15 00:34:48

222

Views

Why this doesn't contradict Monotone and Dominated Convergence Theorem?

Published on 15 Apr 2026 - 0:34

List Question

Limit of $\int_E f(nx) dx$ for a $1$-periodic function $f$ on $[0,2\pi]$

Prove that $\|f\|_p \leq \liminf \|f_n\|_p$ under weak convergence

For a Lebesgue integrable function $f$, the map $t\mapsto\int \chi_{A+t}f(x) dx $ is continuous

If $f ∈ L^1((0, 1))$ is non-negative and $\int_0^1 f=1$, then $\int_0^1 f^{-1}\ge 1$

Integration w.r.t nondegenerate Gaussian probability measure on $X$ with mean $0$

Lebesgue-integrable function particular characteristic

Integral equal $0$ for all $x$ implies $f=0$ a.e.

Prove an equality ($L^P$ spaces)

For which $\alpha, \beta \in \mathbb{R}$ is $\frac{1}{x^\alpha (\log(x))^\beta} \in L^p((1,\infty)$ where $1\leq p \leq \infty$

Hint for Lebesgue theory/functional analysis type of problem

Evaluate Integral of $\int_0^{\frac{\pi 2^n}{2}}\sin^{2+d}(u)\prod_{i=1}^{n}\cos^{2-d}(u/2^i)du$

Find a function $b$ such that the operator $\frac{d}{dx}+b(x)$ is symmetric with the weight $x^2$

Attempting to use dominated convergence theorem

Question about inequality relating infinity norm and Lebesgue integral

Why this doesn't contradict Monotone and Dominated Convergence Theorem?

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