List questions from lebesgue-integral

Published on 09 Apr 2026 - 12:20

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Integration over a variety

Published on 12 Apr 2026 - 6:53

48

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Is this subspace of $L^1(\mathbb{R},m)$ closed?

Published on 14 Apr 2026 - 18:14

92

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If $f \in \mathcal{L}^{2}(\mathbb{R}^{n})$, does it imply that it is bounded almost everywhere?

Published on 15 Apr 2026 - 13:23

340

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Dense subset of $L^p[a,b]$

Published on 15 Apr 2026 - 21:29

1.4k

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Showing that $L^2\subset L^1$ for $L^2([0,t_f])$, with $t_f$ a fixed positive number.

Published on 16 Apr 2026 - 10:29

1.4k

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show Lebesgue dominated convergence theorem fails for ${n^2xe^{-nx}} x\in [0,1]$

Published on 15 Apr 2026 - 15:39

166

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Trying to calculate the integral limit $\lim_{n\rightarrow\infty} \int_{-\sqrt n}^{\sqrt n}\left (1 - \frac{x^2}{2n}\right)^ndx$

Published on 16 Apr 2026 - 18:13

232

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Dominated convergence and fundamental lemma of the calculus of variation

Published on 12 Apr 2026 - 21:06

262

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If $\int f=0$ and $f(x) \ge 0$ for all $x \in \mathbb{R}^d$, then $f=0$ a.e.

Published on 16 Apr 2026 - 15:54

66

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Prove $X$ is a complete vector space $\iff$ $\Big[\quad\sum_{n=1}^\infty \| x_n \| \implies \sum_{n=1}^\infty x_n$ converges$\quad\Big]$

Published on 17 Apr 2026 - 8:08

100

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Definition of Lebesgue integrable function

Published on 11 Apr 2026 - 14:21

98

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how to prove $\int{f}d\mu=\sum_{x\in\Omega}f(x)$

Published on 13 Apr 2026 - 18:00

1.7k

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Limit of the integral $\int_0^1\frac{n\cos x}{1+x^2n^{3/2}}\,dx$

Published on 16 Apr 2026 - 23:06

54

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Comparing limits of integrals

Published on 09 Apr 2026 - 1:02

List Question

property of distribution function

Integration over a variety

Is this subspace of $L^1(\mathbb{R},m)$ closed?

If $f \in \mathcal{L}^{2}(\mathbb{R}^{n})$, does it imply that it is bounded almost everywhere?

Dense subset of $L^p[a,b]$

Showing that $L^2\subset L^1$ for $L^2([0,t_f])$, with $t_f$ a fixed positive number.

show Lebesgue dominated convergence theorem fails for ${n^2xe^{-nx}} x\in [0,1]$

Trying to calculate the integral limit $\lim_{n\rightarrow\infty} \int_{-\sqrt n}^{\sqrt n}\left (1 - \frac{x^2}{2n}\right)^ndx$

Dominated convergence and fundamental lemma of the calculus of variation

If $\int f=0$ and $f(x) \ge 0$ for all $x \in \mathbb{R}^d$, then $f=0$ a.e.

Prove $X$ is a complete vector space $\iff$ $\Big[\quad\sum_{n=1}^\infty \| x_n \| \implies \sum_{n=1}^\infty x_n$ converges$\quad\Big]$

Definition of Lebesgue integrable function

how to prove $\int{f}d\mu=\sum_{x\in\Omega}f(x)$

Limit of the integral $\int_0^1\frac{n\cos x}{1+x^2n^{3/2}}\,dx$

Comparing limits of integrals

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