List questions from measurable-functions

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suppose $ f: \mathbb{R} \rightarrow \mathbb{R}$ is M-measurable, Let E be the set of points at which f is continuous, show that E is M-measurable.

Published on 13 Mar 2019 - 0:03

34

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How to express random inequality events in terms of measurable events?

Published on 25 Mar 2026 - 9:05

1.6k

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Projection of a measurable set of positive measure.

Published on 21 Mar 2019 - 6:03

1.6k

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Show that $f_n$ converges in $L^1$ norm

Published on 23 Mar 2019 - 20:45

42

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σ-algebra and measure of the union of 2 sets. Based on measure theory.

Published on 24 Mar 2019 - 13:44

296

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How to show this function is measurable

Published on 26 Mar 2019 - 15:00

803

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Does piecewise continuous imply Borel measurable?

Published on 25 Mar 2026 - 4:55

70

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Showing that transition is measurable

Published on 25 Mar 2026 - 3:13

93

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Approximate the integral of an unsigned measurable function

Published on 01 Apr 2019 - 2:29

27

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Does taking the limit in one argument preserve regularity in another argument?

Published on 23 Mar 2026 - 11:17

201

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Rigorous construction of the pointwise limit of a sequence of random variables

Published on 22 Mar 2026 - 22:04

302

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Is a function on a product measurable space measurable iff it is componentwise measurable?

Published on 25 Mar 2026 - 7:58

47

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How to map the coefficients of an SDE to its solution process in a measurable way?

Published on 25 Mar 2026 - 11:23

212

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Prove that $g(x):=\int_0^1f(x,y)dy$ is Borel measurable.

Published on 24 Apr 2019 - 14:59

88

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How to go about finding all $\mathcal{F}-$measurable functions

Published on 27 Apr 2019 - 8:10

List Question

suppose $ f: \mathbb{R} \rightarrow \mathbb{R}$ is M-measurable, Let E be the set of points at which f is continuous, show that E is M-measurable.

How to express random inequality events in terms of measurable events?

Projection of a measurable set of positive measure.

Show that $f_n$ converges in $L^1$ norm

σ-algebra and measure of the union of 2 sets. Based on measure theory.

How to show this function is measurable

Does piecewise continuous imply Borel measurable?

Showing that transition is measurable

Approximate the integral of an unsigned measurable function

Does taking the limit in one argument preserve regularity in another argument?

Rigorous construction of the pointwise limit of a sequence of random variables

Is a function on a product measurable space measurable iff it is componentwise measurable?

How to map the coefficients of an SDE to its solution process in a measurable way?

Prove that $g(x):=\int_0^1f(x,y)dy$ is Borel measurable.

How to go about finding all $\mathcal{F}-$measurable functions

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