Question

Establishing a few properties of the lower and upper Lebesgue integral

score 1k · Answer 1 · 2017-01-03 21:54:00

1k

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Establishing a few properties of the lower and upper Lebesgue integral

Published on 03 Jan 2017 - 21:54

score 405 · Answer 2 · 2017-01-04 00:13:27

405

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Disjoint subsets $A$ and $B$ of $\mathbb{R}^n$ such that $\lambda^(A\cup B)<\lambda^(A)+\lambda^*(B)$

Published on 04 Jan 2017 - 0:13

score 98 · Answer 3 · 2017-01-04 04:06:38

98

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Proving $\int f+g \, d\mu=\int f \, d\mu + \int g \, d\mu$ without convergence theorems.

Published on 04 Jan 2017 - 4:06

score 36 · Answer 4 · 2026-03-31 19:16:10

36

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Doubt on properties of Lebesgue and Riemann integrals

Published on 31 Mar 2026 - 19:16

score 669 · Answer 5 · 2017-01-04 14:12:28

669

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$E \subset \mathbb{R}$ such that $\lambda(E \cap [a,b])=\frac{1}{2}(b-a)$ for all $a,b\in\mathbb{R}$

Published on 04 Jan 2017 - 14:12

score 53 · Answer 6 · 2017-01-06 12:13:03

53

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Calculate $\int_0^1 \int_0^1 f(x, y) \ d\lambda(x) \ d\lambda(y)$

Published on 06 Jan 2017 - 12:13

score 568 · Answer 7 · 2026-03-31 19:12:07

568

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Proving Lebesgue Integration Yields Same Answer As Riemann

Published on 31 Mar 2026 - 19:12

score 70 · Answer 8 · 2017-01-06 23:04:41

70

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Lebesgue Dominated Convergence theorem where $x \to x_0$ instead of $ n \to \infty$?

Published on 06 Jan 2017 - 23:04

score 126 · Answer 9 · 2017-01-07 13:56:31

126

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For $K := \{(x, y, z) \in [a, b] \times \Bbb R^2: y^2 + z^2 \le (f(x))^2\}$, prove that $\lambda^3(K) = \pi \int_a^b (f(x))^2 dx$

Published on 07 Jan 2017 - 13:56

score 120 · Answer 10 · 2017-01-07 18:38:55

120

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Is Fubini's theorem the right way to solve this?

Published on 07 Jan 2017 - 18:38

score 64 · Answer 11 · 2017-01-08 05:26:39

64

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$\int_X g(x) d G(E) = \int_X g(x)f(x) d\mu (x)$?

Published on 08 Jan 2017 - 5:26

score 996 · Answer 12 · 2026-03-25 21:48:48

996

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Convergence of sum of random variables' expectations

Published on 25 Mar 2026 - 21:48

score 166 · Answer 13 · 2017-01-08 10:33:39

166

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Integrability of Higher-Dimensional Functions

Published on 08 Jan 2017 - 10:33

score 4.4k · Answer 14 · 2026-04-08 02:46:25

4.4k

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Definition of $L^\infty$

Published on 08 Apr 2026 - 2:46

score 77 · Answer 15 · 2026-04-08 02:39:13

77

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$\mu(X)=\infty$, and $f\in L^p (X)$ for some $1<p<\infty \Longrightarrow f\in L^1 (X)$

Published on 08 Apr 2026 - 2:39

List Question

Establishing a few properties of the lower and upper Lebesgue integral

Disjoint subsets $A$ and $B$ of $\mathbb{R}^n$ such that $\lambda^(A\cup B)<\lambda^(A)+\lambda^*(B)$

Proving $\int f+g \, d\mu=\int f \, d\mu + \int g \, d\mu$ without convergence theorems.

Doubt on properties of Lebesgue and Riemann integrals

$E \subset \mathbb{R}$ such that $\lambda(E \cap [a,b])=\frac{1}{2}(b-a)$ for all $a,b\in\mathbb{R}$

Calculate $\int_0^1 \int_0^1 f(x, y) \ d\lambda(x) \ d\lambda(y)$

Proving Lebesgue Integration Yields Same Answer As Riemann

Lebesgue Dominated Convergence theorem where $x \to x_0$ instead of $ n \to \infty$?

For $K := \{(x, y, z) \in [a, b] \times \Bbb R^2: y^2 + z^2 \le (f(x))^2\}$, prove that $\lambda^3(K) = \pi \int_a^b (f(x))^2 dx$

Is Fubini's theorem the right way to solve this?

$\int_X g(x) d G(E) = \int_X g(x)f(x) d\mu (x)$?

Convergence of sum of random variables' expectations

Integrability of Higher-Dimensional Functions

Definition of $L^\infty$

$\mu(X)=\infty$, and $f\in L^p (X)$ for some $1<p<\infty \Longrightarrow f\in L^1 (X)$

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