Question

Proof verification: Show $t(\mu)$ has density w.r.t. the Lebesgue measure $m_2$ given by $t(\mu)=\int_\mu \hat{f} dm_2$

score 43 · Answer 1 · 2020-01-08 18:36:59

43

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Proof verification: Show $t(\mu)$ has density w.r.t. the Lebesgue measure $m_2$ given by $t(\mu)=\int_\mu \hat{f} dm_2$

Published on 08 Jan 2020 - 18:36

score 1.7k · Answer 2 · 2026-04-10 13:15:21

1.7k

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Finding the measure of the generalized Cantor set.

Published on 10 Apr 2026 - 13:15

score 425 · Answer 3 · 2026-04-11 20:42:43

425

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folland Exercise 2.24

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score 98 · Answer 4 · 2026-04-12 00:52:30

98

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Find a sequence $\left\{f_{n}\right\}$ of Borel measurable functions on $\mathbb{R}$ which...

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score 77 · Answer 5 · 2020-01-11 19:39:37

77

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Is $\lambda^(A \cap B) + \lambda^(A \cup B) \leq \lambda^(A) + \lambda^(B)$ true for all sets

Published on 11 Jan 2020 - 19:39

score 77 · Answer 6 · 2026-03-31 10:37:57

77

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$\{ x \in \mathbb{R} : (\exists c > 1) \liminf n^c ||nx|| < \infty \}$ has zero Lebesgue measure

Published on 31 Mar 2026 - 10:37

score 27 · Answer 7 · 2026-04-08 23:17:44

27

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Wikipedia, complete measure and measure produce

Published on 08 Apr 2026 - 23:17

score 1.1k · Answer 8 · 2026-04-12 13:08:48

1.1k

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A decreasing sequence of Lebesgue measureable sets

Published on 12 Apr 2026 - 13:08

score 348 · Answer 9 · 2026-04-04 03:06:23

348

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Published on 04 Apr 2026 - 3:06

score 30 · Answer 10 · 2020-01-14 19:31:38

30

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$\lim_{n \to \infty} m\{x:|f_n(x)-f(x)||f_n(x)|> \eta\}=0$ under these conditions?

Published on 14 Jan 2020 - 19:31

score 1.1k · Answer 11 · 2026-04-09 18:30:12

1.1k

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Dominated convergence theorem counterexample

Published on 09 Apr 2026 - 18:30

score 65 · Answer 12 · 2026-04-09 13:32:10

65

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Proof Verification: measure theory problem

Published on 09 Apr 2026 - 13:32

score 21 · Answer 13 · 2020-01-16 05:09:19

21

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Do the assumptions give us $\limsup_{n \to \infty} m\{x \in E:|f_{N_n}(x)-f(x)|> \eta\}=0$?

Published on 16 Jan 2020 - 5:09

score 106 · Answer 14 · 2026-04-04 04:40:37

106

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Use dominated convergence theorem to show: $\lim_{\ n \to \infty} \| f \ 1_{[n,n+1]} \|_1 = 0$

Published on 04 Apr 2026 - 4:40

score 122 · Answer 15 · 2020-01-16 19:09:12

122

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Is the preimage of a $[a, b)$ interval under a continuous function $ f: \mathbb{R} \rightarrow \mathbb{R} $ always with measure zero boundary?

Published on 16 Jan 2020 - 19:09

List Question

Proof verification: Show $t(\mu)$ has density w.r.t. the Lebesgue measure $m_2$ given by $t(\mu)=\int_\mu \hat{f} dm_2$

Finding the measure of the generalized Cantor set.

folland Exercise 2.24

Find a sequence $\left\{f_{n}\right\}$ of Borel measurable functions on $\mathbb{R}$ which...

Is $\lambda^(A \cap B) + \lambda^(A \cup B) \leq \lambda^(A) + \lambda^(B)$ true for all sets

$\{ x \in \mathbb{R} : (\exists c > 1) \liminf n^c ||nx|| < \infty \}$ has zero Lebesgue measure

Wikipedia, complete measure and measure produce

A decreasing sequence of Lebesgue measureable sets

Is $\frac{\sin(x)}{x}$ Lebesgue-Integrable?

$\lim_{n \to \infty} m\{x:|f_n(x)-f(x)||f_n(x)|> \eta\}=0$ under these conditions?

Dominated convergence theorem counterexample

Proof Verification: measure theory problem

Do the assumptions give us $\limsup_{n \to \infty} m\{x \in E:|f_{N_n}(x)-f(x)|> \eta\}=0$?

Use dominated convergence theorem to show: $\lim_{\ n \to \infty} \| f \ 1_{[n,n+1]} \|_1 = 0$

Is the preimage of a $[a, b)$ interval under a continuous function $ f: \mathbb{R} \rightarrow \mathbb{R} $ always with measure zero boundary?

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