List questions from lebesgue-measure

Published on 10 Apr 2026 - 9:41

82

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Lebesgue measure as probability

Published on 10 Apr 2026 - 23:23

166

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Computing product measure.

Published on 10 Apr 2026 - 10:17

755

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Continuity Properties of Lebesgue Measure violated by non-measurable sets?

Published on 11 Apr 2026 - 20:57

57

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Lebesgue measure of a set formed by one point from each circumference

Published on 12 Nov 2019 - 1:55

181

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About Lebesgue-measure and regularity.

Published on 09 Apr 2026 - 20:55

765

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A question about Fubini's Theorem

Published on 09 Apr 2026 - 9:53

564

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Show that if f is Lebesgue measurable and f = g almost everywhere with respect to Lebesgue measure, then g is Lebesgue measurble.

Published on 12 Nov 2019 - 12:36

23

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What's the reason for the pre-image def. of Lebesgue measurable?

Published on 11 Apr 2026 - 19:17

273

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The Lebesgue measure satisfies $\lambda(x+E)=\lambda(E)$

Published on 10 Apr 2026 - 11:39

40

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Calculate the Integral of $\int \frac{1}{x+y}d\lambda_2(x,y)$ on $[0,1]^2$

Published on 13 Nov 2019 - 22:08

117

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$\int_\mathbb{R}\psi(t)f(t)dt=0$ for all Lebesgue integrable functions $f$ with $\int_\mathbb{R}f(t)dt=0$ implies $\psi$ is constant

Published on 28 Mar 2026 - 14:06

171

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If $\alpha$ irrational, then $F(x,y)=(x+\alpha,x+y)\mod1$, $T^{2}\to T^{2}$ preserves Lebesgue measure and is not weak mixing

Published on 04 Apr 2026 - 22:43

34

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If $f$ is measured then for every real number a set {$x: f (x) = a$} measured, is the opposite true?

Published on 28 Mar 2026 - 12:14

65

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Example $f\in L^p([0,1]) \backslash L^q([0,1]) $ and $g\in L^p(R) \backslash L^q(R) $?

Published on 02 Apr 2026 - 3:50

List Question

Regular measure

Lebesgue measure as probability

Computing product measure.

Continuity Properties of Lebesgue Measure violated by non-measurable sets?

Lebesgue measure of a set formed by one point from each circumference

About Lebesgue-measure and regularity.

A question about Fubini's Theorem

Show that if f is Lebesgue measurable and f = g almost everywhere with respect to Lebesgue measure, then g is Lebesgue measurble.

What's the reason for the pre-image def. of Lebesgue measurable?

The Lebesgue measure satisfies $\lambda(x+E)=\lambda(E)$

Calculate the Integral of $\int \frac{1}{x+y}d\lambda_2(x,y)$ on $[0,1]^2$

$\int_\mathbb{R}\psi(t)f(t)dt=0$ for all Lebesgue integrable functions $f$ with $\int_\mathbb{R}f(t)dt=0$ implies $\psi$ is constant

If $\alpha$ irrational, then $F(x,y)=(x+\alpha,x+y)\mod1$, $T^{2}\to T^{2}$ preserves Lebesgue measure and is not weak mixing

If $f$ is measured then for every real number a set {$x: f (x) = a$} measured, is the opposite true?

Example $f\in L^p([0,1]) \backslash L^q([0,1]) $ and $g\in L^p(R) \backslash L^q(R) $?

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