List questions from lebesgue-integral

Published on 10 Apr 2026 - 5:51

75

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Find $\lim_{n \to \infty} n^{\alpha} \int_{n}^{\infty} \frac{f(x/n^2)}{x^{\alpha + 1}}(x-n)dx$

Published on 17 Apr 2026 - 9:57

864

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If $f_n$ converges in measure to $f$, prove prove $\lim_{n\to\infty} \int_a^b f_n(x)dx=\int_a^b f(x)dx$.

Published on 17 Apr 2026 - 5:04

511

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The norm $\|f_n-f\|_{L^1} \to 0$ but $f_n \not\to f$

Published on 17 Apr 2026 - 14:57

759

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An example in which the Fubini theorem is inapplicable

Published on 14 Apr 2026 - 13:00

406

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Why is it important that $L^P$ spaces be complete?

Published on 15 Apr 2026 - 6:09

472

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Isn't the statement of the Fatou's lemma somewhat problematic?

Published on 11 Apr 2026 - 19:31

258

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Show that this integral is finite $\lim_n \int_0^n x^p (\ln x)^r \left(1 - \frac{x}{n} \right)^n dx$

Published on 16 Apr 2026 - 16:26

1k

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Application of Monotone Convergence Theorem

Published on 11 Apr 2026 - 7:27

715

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Lebesgue integration by parts in Sobolev space $W^{1,2}(\mathbb{R})$

Published on 14 Apr 2026 - 0:43

567

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Characteristic functions dense in simple functions in $L^1$?

Published on 15 Apr 2026 - 20:29

333

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Lebesgue integral over subset

Published on 10 Apr 2026 - 8:20

230

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Lebesgue integrable function at $[0,+\infty)$

Published on 09 Apr 2026 - 12:02

404

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If a function is Lebesgue measureable, does this imply Lebesgue integrability?

Published on 13 Apr 2026 - 15:44

48

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Sion Minmax theorem for integral operators

Published on 13 Apr 2026 - 12:41

List Question

To show that a function defined by integral is absolutely continuous

Find $\lim_{n \to \infty} n^{\alpha} \int_{n}^{\infty} \frac{f(x/n^2)}{x^{\alpha + 1}}(x-n)dx$

If $f_n$ converges in measure to $f$, prove prove $\lim_{n\to\infty} \int_a^b f_n(x)dx=\int_a^b f(x)dx$.

The norm $\|f_n-f\|_{L^1} \to 0$ but $f_n \not\to f$

An example in which the Fubini theorem is inapplicable

Why is it important that $L^P$ spaces be complete?

Isn't the statement of the Fatou's lemma somewhat problematic?

Show that this integral is finite $\lim_n \int_0^n x^p (\ln x)^r \left(1 - \frac{x}{n} \right)^n dx$

Application of Monotone Convergence Theorem

Lebesgue integration by parts in Sobolev space $W^{1,2}(\mathbb{R})$

Characteristic functions dense in simple functions in $L^1$?

Lebesgue integral over subset

Lebesgue integrable function at $[0,+\infty)$

If a function is Lebesgue measureable, does this imply Lebesgue integrability?

Sion Minmax theorem for integral operators

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