List questions from lebesgue-integral

Published on 16 Apr 2026 - 18:49

30

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Interchange of order of integration for $\int_0^\infty y^{s-1} e^{-ay} \int_0^\infty \frac{\sin(2yx)\cos(\pi x^2)}{\sinh(\pi x)}dx dy $

Published on 22 Apr 2026 - 16:21

94

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Integration with Signed Lebesgue-Stieltjes Measure

Published on 10 Apr 2026 - 4:20

80

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Lebesgue theorem of convergence and the limit of an integral

Published on 09 Apr 2026 - 5:14

151

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If f and g are simple functions such that $f \le g$ then the Lebesgue integral $\int_Xfd\mu \le \int_Xgd\mu$

Published on 25 Mar 2026 - 12:50

75

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Implications of positive Lebesgue integrals.

Published on 13 Apr 2026 - 16:49

313

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Borel measurable function that shows Riemann integral is insufficient

Published on 14 Apr 2026 - 21:04

44

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How determine $\chi_{E} * S$?

Published on 12 Apr 2026 - 2:20

786

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Justifying the change of variables formula $\int_{g(a)}^{g(b)} f(y)dy = \int_a^b f(g(x))g'(x)dx$ for Lebesgue Integration

Published on 14 Apr 2026 - 23:35

277

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Compute $\lim_{n\rightarrow\infty}\int^n_0\frac1n \sin(nx)e^{-x}dx$

Published on 17 Apr 2026 - 2:37

348

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Existence of $k$th moment doesn't imply existence of absolute $k$th moment but what about the expected value?

Published on 17 Apr 2026 - 8:09

309

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The integral of a limit of simple functions

Published on 13 Apr 2026 - 9:31

94

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A lebesgue integrable function is measurable

Published on 15 Apr 2026 - 5:52

56

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Is $g(x) = sin(1/x) \forall x \in \mathbb{R} \setminus \{0\}$ and $g(0) = 0$ Lebesgue integrable?

Published on 15 Apr 2026 - 17:16

241

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Prove Lebesgue Integral is between measure of the space times the inf and sup of function

Published on 12 Apr 2026 - 9:57

List Question

Different measures having the equal integrals

Interchange of order of integration for $\int_0^\infty y^{s-1} e^{-ay} \int_0^\infty \frac{\sin(2yx)\cos(\pi x^2)}{\sinh(\pi x)}dx dy $

Integration with Signed Lebesgue-Stieltjes Measure

Lebesgue theorem of convergence and the limit of an integral

If f and g are simple functions such that $f \le g$ then the Lebesgue integral $\int_Xfd\mu \le \int_Xgd\mu$

Implications of positive Lebesgue integrals.

Borel measurable function that shows Riemann integral is insufficient

How determine $\chi_{E} * S$?

Justifying the change of variables formula $\int_{g(a)}^{g(b)} f(y)dy = \int_a^b f(g(x))g'(x)dx$ for Lebesgue Integration

Compute $\lim_{n\rightarrow\infty}\int^n_0\frac1n \sin(nx)e^{-x}dx$

Existence of $k$th moment doesn't imply existence of absolute $k$th moment but what about the expected value?

The integral of a limit of simple functions

A lebesgue integrable function is measurable

Is $g(x) = sin(1/x) \forall x \in \mathbb{R} \setminus \{0\}$ and $g(0) = 0$ Lebesgue integrable?

Prove Lebesgue Integral is between measure of the space times the inf and sup of function

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