List questions from lebesgue-integral

Published on 16 Apr 2026 - 12:12

59

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Show that: $ \lambda_3(K) = \pi \int_{a}^{b} f(x)^2 dx$. Why is $\lambda_2(K_x)$ = $\pi \cdot f(x)^2 $? $K_x$ circle with radius of $f(x)$

Published on 17 Apr 2026 - 8:16

91

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Show that $g$ is integrable and that $\int_E f\,d\mu = \int_E g \,d\mu, \,\,E\in\mathcal{A}.$

Published on 16 Apr 2026 - 23:30

183

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Show that $\int\limits_{[a,b]}fd\lambda = \int\limits_{(a,b)} fd\lambda$, for $-\infty<a,b<\infty$.

Published on 14 Apr 2026 - 11:30

666

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$|\mu|(E) = \sup\{|\int_E f\,d\mu | ; |f|\leq 1 \}$, total variation of a measure.

Published on 12 Apr 2026 - 21:53

33

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Sufficient condition for convergence in $L^1$

Published on 11 Apr 2026 - 17:12

193

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Show that $f$ is integrable iff $\sum\limits_{n\in\mathbb{Z}}2^n \mu(\{x\in S:2^n< \left|f(x)\right|\leq2^{n+1}\})<\infty.$

Published on 15 Apr 2026 - 20:50

119

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A probabilistic average integral

Published on 11 Apr 2026 - 19:09

96

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Does this kind of $C^1$-diffeomorphism a contraction?

Published on 13 Apr 2026 - 16:39

69

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Is $f(0)$ finite?

Published on 14 Apr 2026 - 4:40

102

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Calculate $\int_{\Omega}f d\lambda$.

Published on 14 Apr 2026 - 23:12

66

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Fubini in $\mathbb{R^2}$

Published on 11 Apr 2026 - 14:57

76

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Area under this chaotic function. Is it possible.

Published on 09 Apr 2026 - 15:59

45

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Does the set of points where Lebesgue Stieljes distribution function have zero derivative have zero $ \mu$ measure?

Published on 10 Apr 2026 - 20:10

57

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Why is this function holomorphic in $K(a,\rho)$?

Published on 13 Apr 2026 - 17:49

List Question

$\int_{\mathbb{R}}\mu((A-x) \cap B)d\mu = \mu(A)\mu(B)$

Show that: $ \lambda_3(K) = \pi \int_{a}^{b} f(x)^2 dx$. Why is $\lambda_2(K_x)$ = $\pi \cdot f(x)^2 $? $K_x$ circle with radius of $f(x)$

Show that $g$ is integrable and that $\int_E f\,d\mu = \int_E g \,d\mu, \,\,E\in\mathcal{A}.$

Show that $\int\limits_{[a,b]}fd\lambda = \int\limits_{(a,b)} fd\lambda$, for $-\infty<a,b<\infty$.

$|\mu|(E) = \sup\{|\int_E f\,d\mu | ; |f|\leq 1 \}$, total variation of a measure.

Sufficient condition for convergence in $L^1$

Show that $f$ is integrable iff $\sum\limits_{n\in\mathbb{Z}}2^n \mu(\{x\in S:2^n< \left|f(x)\right|\leq2^{n+1}\})<\infty.$

A probabilistic average integral

Does this kind of $C^1$-diffeomorphism a contraction?

Is $f(0)$ finite?

Calculate $\int_{\Omega}f d\lambda$.

Fubini in $\mathbb{R^2}$

Area under this chaotic function. Is it possible.

Does the set of points where Lebesgue Stieljes distribution function have zero derivative have zero $ \mu$ measure?

Why is this function holomorphic in $K(a,\rho)$?

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