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 494 · Answer 1 · 2026-03-25 07:45:41

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 851 · Answer 2 · 2026-04-06 02:32:10

851

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score 88 · Answer 5 · 2026-04-09 23:20:13

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score 53 · Answer 7 · 2026-05-07 16:19:52

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score 49 · Answer 13 · 2026-04-30 02:29:30

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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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