Question

Can I apply measure theory in non-mathematics fields?

score 48 · Answer 1 · 2026-04-09 19:39:35

48

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Can I apply measure theory in non-mathematics fields?

Published on 09 Apr 2026 - 19:39

score 87 · Answer 2 · 2026-04-16 00:53:03

87

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Let A be a measurable set in R. Let B be all of it's densed points. is B necessarily open?

Published on 16 Apr 2026 - 0:53

score 1.1k · Answer 3 · 2026-04-11 22:45:02

1.1k

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Lebesgue point of density on $[0,1]$ and Dynkin's theorem

Published on 11 Apr 2026 - 22:45

score 325 · Answer 4 · 2026-04-08 19:43:35

325

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Help with a Royden exercise of measure

Published on 08 Apr 2026 - 19:43

score 65 · Answer 5 · 2026-04-15 03:12:31

65

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Prove that $\int_{[c,d]}|f(x,y)|d\mathcal{L}(y)<\infty$ for $\mathcal{L}$-almost all $x\in [a,b]$.

Published on 15 Apr 2026 - 3:12

score 348 · Answer 6 · 2026-04-12 10:21:32

348

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How to prove product of measurable set is measurable using dynkin's $\pi-\lambda$ theorem?

Published on 12 Apr 2026 - 10:21

score 195 · Answer 7 · 2026-04-14 14:52:09

195

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Lebesgue Measure in ${R}^m$

Published on 14 Apr 2026 - 14:52

score 142 · Answer 8 · 2026-04-15 21:30:33

142

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Royden - section 4.2, page 73 - linearity

Published on 15 Apr 2026 - 21:30

score 52 · Answer 9 · 2026-04-15 02:40:57

52

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For every $E \subseteq \mathbb{R}^d$ with $0 < |E|_e < \infty$ and $0 < a < 1$ there exists a cube Q such that $|E \cap Q|_e \geq a|Q|$

Published on 15 Apr 2026 - 2:40

score 76 · Answer 10 · 2026-04-15 07:25:50

76

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Show that $\mu$ is absolutely continuous w.r.t. $\mathcal{L}$ and find $\frac{d\mu} {d\mathcal{L}}$

Published on 15 Apr 2026 - 7:25

score 41 · Answer 11 · 2026-04-15 03:09:00

41

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Non-negative Lebesgue Measurable Functions/Determining Measure of a Particular Set

Published on 15 Apr 2026 - 3:09

score 88 · Answer 12 · 2026-04-16 15:18:45

88

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Convergence of $f_n(x) = 2^n \cdot F(2^n (x-a_n))$ with $F(x) = e^{-x^2}$ with different notions of convergence.

Published on 16 Apr 2026 - 15:18

score 1.2k · Answer 13 · 2026-04-16 15:48:45

1.2k

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$f$ is Riemann integrable iif the set of discontinuous points of $f$ has Lebesgue measure zero

Published on 16 Apr 2026 - 15:48

score 601 · Answer 14 · 2026-04-15 02:55:58

601

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Use Dominated convergence theorem to show that $f(x):=\sum_{k=1}^{\infty}\frac{\cos(kx)}{k^3}$ is differentiable

Published on 15 Apr 2026 - 2:55

score 1.7k · Answer 15 · 2026-04-13 17:31:09

1.7k

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What can you say about union of two non measurable set. They are measurable or not?

Published on 13 Apr 2026 - 17:31

List Question

Can I apply measure theory in non-mathematics fields?

Let A be a measurable set in R. Let B be all of it's densed points. is B necessarily open?

Lebesgue point of density on $[0,1]$ and Dynkin's theorem

Help with a Royden exercise of measure

Prove that $\int_{[c,d]}|f(x,y)|d\mathcal{L}(y)<\infty$ for $\mathcal{L}$-almost all $x\in [a,b]$.

How to prove product of measurable set is measurable using dynkin's $\pi-\lambda$ theorem?

Lebesgue Measure in ${R}^m$

Royden - section 4.2, page 73 - linearity

For every $E \subseteq \mathbb{R}^d$ with $0 < |E|_e < \infty$ and $0 < a < 1$ there exists a cube Q such that $|E \cap Q|_e \geq a|Q|$

Show that $\mu$ is absolutely continuous w.r.t. $\mathcal{L}$ and find $\frac{d\mu} {d\mathcal{L}}$

Non-negative Lebesgue Measurable Functions/Determining Measure of a Particular Set

Convergence of $f_n(x) = 2^n \cdot F(2^n (x-a_n))$ with $F(x) = e^{-x^2}$ with different notions of convergence.

$f$ is Riemann integrable iif the set of discontinuous points of $f$ has Lebesgue measure zero

Use Dominated convergence theorem to show that $f(x):=\sum_{k=1}^{\infty}\frac{\cos(kx)}{k^3}$ is differentiable

What can you say about union of two non measurable set. They are measurable or not?

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