List questions from measurable-functions

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Measure theory, confused over which definition to use

Published on 14 Mar 2020 - 8:49

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Show that a line segment is Jordan measurable.

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Composition of inverse of measurable functions

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Consider a measure space $(X,\mathcal{M},\mu$).

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Show a step function is measurable

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if $f$ is measurable real valued function on $E \subseteq \mathbb{R}^n$ then $f^{-1} (B)$ is borel set for every borel set in $\mathbb{R}$?

Published on 25 Mar 2020 - 17:01

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Suppose $\{f_t\}$ is an uncountable family of measurable functions , then can we show that $F(x):=\sup_t f_t(x)$ measurable?

Published on 26 Mar 2020 - 16:36

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Showing that a function is measurable

Published on 29 Mar 2020 - 8:13

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I can't understand why characteristic functions are measurable

Published on 29 Mar 2020 - 22:59

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If $f=f_{1}-f_{2}$ with $f_{1},f_{2}\geq0$ a.e. then $f_{1}=f^{+}$ and $f_{2}=f^{-}$? (measure theory)

Published on 30 Mar 2020 - 20:12

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How to prove the graph of a continuous on a closed interval is measurable?

Published on 31 Mar 2020 - 7:40

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How do we define an "intuitive" average on this function?

Published on 28 Mar 2026 - 15:10

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Mean Value Theorem for measurable functions

Published on 05 Apr 2020 - 7:45

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$\int f\,d\mu<\infty\Leftrightarrow\sum_{n=0}^\infty\frac{1}{2^n}\mu\left(\left\{x\in X:f(x)\geq\frac{1}{2^n}\right\}\right)<\infty$

Published on 06 Apr 2020 - 5:48

List Question

Use of inverse in defining Lebesgue measure

Measure theory, confused over which definition to use

Show that a line segment is Jordan measurable.

Composition of inverse of measurable functions

Consider a measure space $(X,\mathcal{M},\mu$).

Show a step function is measurable

if $f$ is measurable real valued function on $E \subseteq \mathbb{R}^n$ then $f^{-1} (B)$ is borel set for every borel set in $\mathbb{R}$?

Suppose $\{f_t\}$ is an uncountable family of measurable functions , then can we show that $F(x):=\sup_t f_t(x)$ measurable?

Showing that a function is measurable

I can't understand why characteristic functions are measurable

If $f=f_{1}-f_{2}$ with $f_{1},f_{2}\geq0$ a.e. then $f_{1}=f^{+}$ and $f_{2}=f^{-}$? (measure theory)

How to prove the graph of a continuous on a closed interval is measurable?

How do we define an "intuitive" average on this function?

Mean Value Theorem for measurable functions

$\int f\,d\mu<\infty\Leftrightarrow\sum_{n=0}^\infty\frac{1}{2^n}\mu\left(\left\{x\in X:f(x)\geq\frac{1}{2^n}\right\}\right)<\infty$

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