List questions from lebesgue-integral

Published on 17 Apr 2026 - 16:04

113

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Norm of a linear functional in $L^2[0, 10]$.

Published on 13 Apr 2026 - 7:44

548

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Lebesgue integral over $\mathbb{R}$

Published on 10 Apr 2026 - 12:27

214

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Example of a Borel measurable function $f: [a,b] \to \Bbb{R}$ that is not integrable w.r.t. Borel sets but is w.r.t.Lebesgue measurable sets

Published on 15 Apr 2026 - 19:39

527

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Evaluate $\lim_{k \to \infty} \int_0^1 \frac{(1-x)^k \cos(k/x)}{\sqrt{x}}dx$

Published on 17 Apr 2026 - 9:50

376

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Integral of indicator function

Published on 11 Apr 2026 - 21:31

175

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Prove that $F(x)=\int_{x_{1}^{0}}^{x_1}\cdots \int_{x_{n}^{0}}^{x_n} f(y) \, dy_1 \cdots dy_n$ is continuous

Published on 16 Apr 2026 - 2:40

450

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Continuous function is absolutely continuous on [0,1] if it is increasing

Published on 12 Apr 2026 - 9:45

133

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Integral involving distance to the boundary

Published on 13 Apr 2026 - 10:29

410

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$L^1$ convergence for convex combinations of non-negative random variables

Published on 13 Apr 2026 - 20:20

170

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Bounded real-valued function on $[0,1]$, non integrable?

Published on 24 Apr 2026 - 12:53

184

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Can I pass the limit under the integral?

Published on 08 Apr 2026 - 6:56

93

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Iff conditions for a $C^1$-diffeomorphism to have $L^1$ or $L^\infty$ Jacobian

Published on 18 Apr 2026 - 9:45

164

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Deriving the value of $\int\limits_{-\infty}^\infty \frac{\sin(x)}{x} dx$ by way of Fourier transformation

Published on 16 Apr 2026 - 23:17

91

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Lebesgue Integral of Lebesgue Measure Function

Published on 10 Apr 2026 - 23:23

List Question

Evaluate $\lim_{n \to \infty} \int_{0}^{n} \frac{\cos(x/n)}{\sqrt{x+\cos(x/n)}}dx$

Norm of a linear functional in $L^2[0, 10]$.

Lebesgue integral over $\mathbb{R}$

Example of a Borel measurable function $f: [a,b] \to \Bbb{R}$ that is not integrable w.r.t. Borel sets but is w.r.t.Lebesgue measurable sets

Evaluate $\lim_{k \to \infty} \int_0^1 \frac{(1-x)^k \cos(k/x)}{\sqrt{x}}dx$

Integral of indicator function

Prove that $F(x)=\int_{x_{1}^{0}}^{x_1}\cdots \int_{x_{n}^{0}}^{x_n} f(y) \, dy_1 \cdots dy_n$ is continuous

Continuous function is absolutely continuous on [0,1] if it is increasing

Integral involving distance to the boundary

$L^1$ convergence for convex combinations of non-negative random variables

Bounded real-valued function on $[0,1]$, non integrable?

Can I pass the limit under the integral?

Iff conditions for a $C^1$-diffeomorphism to have $L^1$ or $L^\infty$ Jacobian

Deriving the value of $\int\limits_{-\infty}^\infty \frac{\sin(x)}{x} dx$ by way of Fourier transformation

Lebesgue Integral of Lebesgue Measure Function

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