List questions from lebesgue-integral

Published on 13 Apr 2026 - 12:04

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$L^{\infty}$ norm

Published on 11 Apr 2026 - 23:24

1.2k

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Convolution with standard mollifier

Published on 09 Apr 2026 - 23:56

29

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Prove that $\frac{\langle f^2,g\rangle_{L^2}}{\left\|f\right\|_{L^2}^2}\ge-\left\|g\right\|_{L^\infty}$ for $f\in L^2$ and $g\in L^\infty$

Published on 17 Apr 2026 - 12:18

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Let $(X,Σ,μ)$ be a measure space and $f$ and $g$ are positive integrable functions and $h=f-g$

Published on 15 Apr 2026 - 22:56

135

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If one side of $\int f\ d\lambda = \int f\ d\mu - \int f\ d\nu$ exists, does the other one exist as well?

Published on 14 Apr 2026 - 22:33

376

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Prove that $\iint\limits_ {[0,1] \times [0,1]} \frac{x^2-y^2}{(x^2 + y^2)^2}\,\mathrm dx\,\mathrm dy$ is not integrable

Published on 15 Apr 2026 - 12:32

133

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How can I prove that $f$ and $g$ are measurable functions

Published on 13 Apr 2026 - 3:43

109

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Is my proof of closedness of multiplication operator corect?

Published on 09 Apr 2026 - 20:30

92

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If the right side of $\int f\ d\lambda = \int f\ d\mu − \int f\ d\nu$ exists, does the left one exist as well?

Published on 16 Apr 2026 - 3:33

908

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Question about the Riemann-Lebesgue Lemma proof

Published on 14 Apr 2026 - 22:09

44

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A kernel to guarantee integrability

Published on 08 Apr 2026 - 22:22

2.1k

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Does convergence in H1 imply pointwise convergence?

Published on 09 Apr 2026 - 2:07

283

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A weaker form of Lebesgue's differentiation theorem in $\Bbb R ^n$

Published on 14 Apr 2026 - 2:14

205

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$f_n \rightarrow 0$ weakly if and only if $(\|f_n\|)_{n=1}^{\infty}$ is bounded and $f_n$ converges pointwise to $0$.

Published on 17 Apr 2026 - 0:36

List Question

Lebesgue differentiation

$L^{\infty}$ norm

Convolution with standard mollifier

Prove that $\frac{\langle f^2,g\rangle_{L^2}}{\left\|f\right\|_{L^2}^2}\ge-\left\|g\right\|_{L^\infty}$ for $f\in L^2$ and $g\in L^\infty$

Let $(X,Σ,μ)$ be a measure space and $f$ and $g$ are positive integrable functions and $h=f-g$

If one side of $\int f\ d\lambda = \int f\ d\mu - \int f\ d\nu$ exists, does the other one exist as well?

Prove that $\iint\limits_ {[0,1] \times [0,1]} \frac{x^2-y^2}{(x^2 + y^2)^2}\,\mathrm dx\,\mathrm dy$ is not integrable

How can I prove that $f$ and $g$ are measurable functions

Is my proof of closedness of multiplication operator corect?

If the right side of $\int f\ d\lambda = \int f\ d\mu − \int f\ d\nu$ exists, does the left one exist as well?

Question about the Riemann-Lebesgue Lemma proof

A kernel to guarantee integrability

Does convergence in H1 imply pointwise convergence?

A weaker form of Lebesgue's differentiation theorem in $\Bbb R ^n$

$f_n \rightarrow 0$ weakly if and only if $(\|f_n\|)_{n=1}^{\infty}$ is bounded and $f_n$ converges pointwise to $0$.

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