List questions from lebesgue-integral

Published on 08 Apr 2026 - 13:25

400

Views

If $\int_{[a,b]} f=0$ , then $\int_E f=0 $ for any measurable $E \subseteq \mathbb{ R}$

Published on 03 Feb 2017 - 4:35

88

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Maximum of finite $L^p$ functions is in $L^p$.

Published on 08 Apr 2026 - 9:21

170

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How can I show that $\lim_{|h|\to 0}\| f(x+h)-f(x)\|_p = 0$?

Published on 08 Apr 2026 - 7:42

151

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Help to understand a passage on a proof ($\|f\|_p\to\|f\|_\infty$).

Published on 04 Feb 2017 - 17:41

55

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Is the given function Lebesgue Integrable?

Published on 09 Apr 2026 - 0:55

210

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Continuity and integration using Dominated Convergence theorem

Published on 07 Apr 2026 - 21:43

540

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Why is the notation $\mu(dt)$ in integrals so widely used in Measure Theory?

Published on 07 Feb 2017 - 16:49

56

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Why is $\int_{[x,y]}| f |\leq |x-y| \int_{R}| f| $?

Published on 08 Feb 2017 - 19:31

515

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Using translational invariance of Lebesgue integrals to check integrability?

Published on 08 Apr 2026 - 17:49

38

Views

Dominated convergence theorem for singular function

Published on 09 Feb 2017 - 10:49

200

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Lebesgue integral, changing the sigma algebra

Published on 09 Feb 2017 - 15:08

728

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Differentiation under the integral sign and uniform integrability

Published on 26 Mar 2026 - 9:48

33

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Suitable factor to set integral to zero

Published on 27 Mar 2026 - 11:45

136

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Conclude that $\sigma$ is a measure on the manifold $E := \{x \in \Bbb R^5: x_1, x_2 \in \Bbb R, x_3 = x_1 + x_2, x_4 = 1, x_5 = 2\}$

Published on 10 Feb 2017 - 12:58

List Question

Integration over an arbitrary triangle / Change-of-variables formula

If $\int_{[a,b]} f=0$ , then $\int_E f=0 $ for any measurable $E \subseteq \mathbb{ R}$

Maximum of finite $L^p$ functions is in $L^p$.

How can I show that $\lim_{|h|\to 0}\| f(x+h)-f(x)\|_p = 0$?

Help to understand a passage on a proof ($\|f\|_p\to\|f\|_\infty$).

Is the given function Lebesgue Integrable?

Continuity and integration using Dominated Convergence theorem

Why is the notation $\mu(dt)$ in integrals so widely used in Measure Theory?

Why is $\int_{[x,y]}| f |\leq |x-y| \int_{R}| f| $?

Using translational invariance of Lebesgue integrals to check integrability?

Dominated convergence theorem for singular function

Lebesgue integral, changing the sigma algebra

Differentiation under the integral sign and uniform integrability

Suitable factor to set integral to zero

Conclude that $\sigma$ is a measure on the manifold $E := \{x \in \Bbb R^5: x_1, x_2 \in \Bbb R, x_3 = x_1 + x_2, x_4 = 1, x_5 = 2\}$

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