List questions from lebesgue-integral

Published on 25 Jul 2019 - 1:01

55

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Proving the function $x$ is integrable over a given set

Published on 26 Jul 2019 - 12:20

60

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Prove this function is locally unbounded, $\sum_n e^{-n^2(x-q_n)^2}$

Published on 26 Jul 2019 - 21:43

39

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Question about the existence of a Lebesgue measurable set

Published on 27 Jul 2019 - 13:55

67

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Theorems of Lebesgue integration theory which is useful for calculating integral

Published on 28 Jul 2019 - 8:54

63

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Exponential decay of solution in $L^p$ with $p>2$

Published on 28 Jul 2019 - 19:35

168

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Nonnegativity of solution of $u_t=\Delta u+u$

Published on 25 Mar 2026 - 17:39

53

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Proof $\mu(E)=0 \rightarrow \int_E f d\mu=0$ 1

Published on 01 Aug 2019 - 8:39

240

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Are Lebesgue integrals equivalent to Daniell integrals?

Published on 01 Aug 2019 - 13:02

73

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$|\{ |f| > t \}| \leq Ct^{-2} \implies \int_{E}|f| \leq D\sqrt{|E|}$

Published on 25 Mar 2026 - 21:47

183

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weak convergence in $L^2$ and convergence of integral involving test-functions

Published on 29 Mar 2026 - 18:14

2.1k

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Lebesgue integrable function is essentially bounded?

Published on 05 Aug 2019 - 6:46

66

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Find a necessary and sufficient condition for the integrabiity of a function

Published on 05 Aug 2019 - 19:01

277

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Weak derivative under the integral sign

Published on 25 Mar 2026 - 17:36

93

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About the Lebesgue integrability of $f$

Published on 06 Aug 2019 - 17:56

List Question

Show that $\int_{\mathbb R^d}(|f_n|^p-|f_n-f|^p)\,dx\to\int_{\mathbb R^d}|f|^p\,dx.$

Proving the function $x$ is integrable over a given set

Prove this function is locally unbounded, $\sum_n e^{-n^2(x-q_n)^2}$

Question about the existence of a Lebesgue measurable set

Theorems of Lebesgue integration theory which is useful for calculating integral

Exponential decay of solution in $L^p$ with $p>2$

Nonnegativity of solution of $u_t=\Delta u+u$

Proof $\mu(E)=0 \rightarrow \int_E f d\mu=0$ 1

Are Lebesgue integrals equivalent to Daniell integrals?

$|\{ |f| > t \}| \leq Ct^{-2} \implies \int_{E}|f| \leq D\sqrt{|E|}$

weak convergence in $L^2$ and convergence of integral involving test-functions

Lebesgue integrable function is essentially bounded?

Find a necessary and sufficient condition for the integrabiity of a function

Weak derivative under the integral sign

About the Lebesgue integrability of $f$

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