Question

If $f:X\to \mathbb C$ is measurable simple function and $f\in L^p$, then $\mu(\{x\mid f(x)\neq 0\})<\infty$.

score 43 · Answer 1 · 2023-03-23 14:33:28

43

Views

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Published on 23 Mar 2023 - 14:33

score 59 · Answer 2 · 2023-05-12 09:55:31

59

Views

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score 48 · Answer 3 · 2023-05-26 12:13:46

48

Views

About Theorem 3.13 integral-type sums for simple functions in "Measure, Integration & Real Analysis" by Sheldon Axler.

Published on 26 May 2023 - 12:13

score 172 · Answer 4 · 2023-05-27 10:48:40

172

Views

Need to use the standard representation of a simple function to prove Theorem 3.13? ("Measure, Integration & Real Analysis" by Sheldon Axler.)

Published on 27 May 2023 - 10:48

score 87 · Answer 5 · 2023-08-09 23:35:55

87

Views

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score 316 · Answer 6 · 2023-09-29 13:05:16

316

Views

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Published on 29 Sep 2023 - 13:05

score 18 · Answer 7 · 2026-03-19 23:07:51

18

Views

Uniform convergence of increasing sequence of simple functions

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score 68 · Answer 8 · 2023-11-24 00:38:27

68

Views

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score 40 · Answer 9 · 2023-12-07 13:20:51

40

Views

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Published on 07 Dec 2023 - 13:20

score 149 · Answer 10 · 2023-12-11 12:26:08

149

Views

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Published on 11 Dec 2023 - 12:26

score 18 · Answer 11 · 2024-02-09 10:24:40

18

Views

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score 15 · Answer 12 · 2026-03-04 19:33:41

15

Views

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score 55 · Answer 13 · 2024-03-31 12:08:42

55

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score 57 · Answer 14 · 2015-02-16 10:53:22

57

Views

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Published on 16 Feb 2015 - 10:53

score 159 · Answer 15 · 2015-03-22 07:51:05

159

Views

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Published on 22 Mar 2015 - 7:51

List Question

If $f:X\to \mathbb C$ is measurable simple function and $f\in L^p$, then $\mu(\{x\mid f(x)\neq 0\})<\infty$.

Approximating the exponential function with simple functions

About Theorem 3.13 integral-type sums for simple functions in "Measure, Integration & Real Analysis" by Sheldon Axler.

Need to use the standard representation of a simple function to prove Theorem 3.13? ("Measure, Integration & Real Analysis" by Sheldon Axler.)

Is there a simple function mapping -1 to 1 and 1 to 0

Why is the average of $\sin^2 wt = 1/2$ and $\cos^2 wt = 1/2$

Uniform convergence of increasing sequence of simple functions

Show $f: X \rightarrow \mathbb R^n$ is measurable iff condition holds

Can we compare simple functions without looking at their values at specific points?

Divergence for original function implies large value eventually for some simple function approximation

Simple functions convergence under different topologies

Hardy-Littlewood maximal function algorithm

Detail in standard measure theory I cannot seem to obtain

Help completing proof that there is an increasing sequence of measurable simple functions to a measurable function.

How to use a simple function in Stieltjes integral to approximate Riemann integral?

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