Question

Show there exist simple functions $s_n$ increasing to $f$ at each point such that $\mu(\left\lbrace x:s_n(x)\neq 0\right\rbrace)<\infty$

score 493 · Answer 1 · 2015-09-22 14:55:41

Show there exist simple functions $s_n$ increasing to $f$ at each point such that $\mu(\left\lbrace x:s_n(x)\neq 0\right\rbrace)<\infty$

score 849 · Answer 2 · 2015-09-23 20:00:11

849

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Simple measurable functions properties

Published on 23 Sep 2015 - 20:00

score 869 · Answer 3 · 2026-02-22 21:09:48

869

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If $f$ and $g$ are Riemann integrable, then $fg$ is Riemann Integrable (with a twist).

Published on 22 Feb 2026 - 21:09

score 35 · Answer 4 · 2015-11-16 07:12:18

35

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Prove the following statement (existence of simple function)

Published on 16 Nov 2015 - 7:12

score 86 · Answer 5 · 2015-12-14 10:47:35

86

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Ito integral via simple process when the integrand is C^1

Published on 14 Dec 2015 - 10:47

score 268 · Answer 6 · 2026-03-03 00:58:47

268

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score 49 · Answer 7 · 2026-03-10 15:54:54

49

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score 217 · Answer 8 · 2026-03-23 00:30:54

217

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score 173 · Answer 9 · 2026-03-18 03:04:10

173

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score 52 · Answer 10 · 2016-04-28 11:15:28

52

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score 56 · Answer 11 · 2026-03-07 11:04:26

56

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small shift in domain of simple function

Published on 07 Mar 2026 - 11:04

score 9.8k · Answer 12 · 2016-05-11 02:01:45

9.8k

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score 44 · Answer 13 · 2026-03-24 22:26:29

44

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Published on 24 Mar 2026 - 22:26

score 162 · Answer 14 · 2016-05-14 20:11:17

162

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score 1.8k · Answer 15 · 2016-06-06 06:15:47

1.8k

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Can every function $f$ be written as the limit of simple functions?

Published on 06 Jun 2016 - 6:15

List Question

Show there exist simple functions $s_n$ increasing to $f$ at each point such that $\mu(\left\lbrace x:s_n(x)\neq 0\right\rbrace)<\infty$

Simple measurable functions properties

If $f$ and $g$ are Riemann integrable, then $fg$ is Riemann Integrable (with a twist).

Prove the following statement (existence of simple function)

Ito integral via simple process when the integrand is C^1

Tao's explanation on how to avoid disjointness for definition of simple function in derivation of Lebesgue Integral

Lebesgue integral confusion

approximating functions via a piecewise combination of linear and constant functions

General set in product space approximated by rectangle sets

Isolating within a simple equation

small shift in domain of simple function

How to prove that if $f$ is continuous a.e., then it is measurable.

approximate a measurable function by simples measuring where they differ over an epsilon

Lebesgue Integral-Question

Can every function $f$ be written as the limit of simple functions?

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