List questions from lebesgue-integral

179

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Suppose that for all $g\in L^2(\mathbb{R}^d)$ we have $\int f_{n}g \to \int fg $. Prove convergence in $L^2$ problem.

Published on 16 Apr 2026 - 11:52

3.3k

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$L^p$-norm of a non-negative measurable function

Published on 10 Apr 2026 - 14:02

199

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Lebesgue Integration problem

Published on 08 Apr 2026 - 17:13

1.2k

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Derivative of step functions

Published on 10 Apr 2026 - 22:32

290

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A question about integral operator

Published on 08 Apr 2026 - 20:02

175

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Convergence in $L^1$ problem.

Published on 13 Apr 2026 - 10:56

208

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Does $f_n \to 0$ in $L^1(\mathbb R^2)$ imply that $f_{n_k}(x,\cdot)\to 0$ in $L^1(\mathbb R)$ for almost every $x \in \mathbb R$?

Published on 16 Apr 2026 - 7:06

1.1k

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Application of Radon Nikodym Theorem on Absolutely Continuous Measures

Published on 11 Apr 2026 - 10:50

88

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Lebesgue integration for $u \in C^{\infty}_c$

Published on 14 Apr 2026 - 5:38

353

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Lebesgue generalizations of Hilbert spaces?

Published on 12 Apr 2026 - 4:58

388

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Another definition of Lebesgue integral

Published on 10 Apr 2026 - 12:04

653

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Yet another definition of Lebesgue integral

Published on 08 Apr 2026 - 21:35

1.6k

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Lebesgue Integration fundamental questions

Published on 08 Apr 2026 - 23:36

215

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Compact set in all $L_p$, $1\leq p<\infty$

Published on 14 Apr 2026 - 20:16

263

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Superposition operator in Sobolev spaces

Published on 04 May 2026 - 9:59

List Question

Suppose that for all $g\in L^2(\mathbb{R}^d)$ we have $\int f_{n}g \to \int fg $. Prove convergence in $L^2$ problem.

$L^p$-norm of a non-negative measurable function

Lebesgue Integration problem

Derivative of step functions

A question about integral operator

Convergence in $L^1$ problem.

Does $f_n \to 0$ in $L^1(\mathbb R^2)$ imply that $f_{n_k}(x,\cdot)\to 0$ in $L^1(\mathbb R)$ for almost every $x \in \mathbb R$?

Application of Radon Nikodym Theorem on Absolutely Continuous Measures

Lebesgue integration for $u \in C^{\infty}_c$

Lebesgue generalizations of Hilbert spaces?

Another definition of Lebesgue integral

Yet another definition of Lebesgue integral

Lebesgue Integration fundamental questions

Compact set in all $L_p$, $1\leq p<\infty$

Superposition operator in Sobolev spaces

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