List questions from borel-measures

35

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Prove that $e^{-x}I(x \geq 0)$ is a measurable function in the Lebesgue measure space given by $(R, \mathcal{B}, \lambda)$

Published on 15 Apr 2026 - 19:01

38

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Is my proof of uniform exterior regularity of Lebesgue measure correct?

Published on 13 Apr 2026 - 16:02

254

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Existence of increasing sequence of compact sets

Published on 09 Apr 2026 - 6:06

48

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On the definition of bounded variation

Published on 12 Apr 2026 - 7:33

1.3k

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Any translation invariant Borel measure such that $\mu([0,1))=1$ is identical to the Lebesgue measure

Published on 16 Apr 2026 - 4:29

29

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Are $\phi(X^2)$ and $\psi(Y^2)$ always independent where $\phi$ and $\psi$ are Borel-Measurable functions (X,Y are any two RVs)?

Published on 02 Oct 2019 - 17:18

68

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Is any continuous functions between Hausdorff spaces measurable wrt. the Borel algebras?

Published on 29 Apr 2026 - 18:37

226

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Compact support of measure.

Published on 10 May 2026 - 15:08

378

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Question on Borel Measurable Functions and Borel Sigma Algebras.

Published on 12 Apr 2026 - 8:26

242

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f(X) and f(Y) are identically distributed

Published on 05 May 2026 - 6:15

69

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Prove that a set is a Borel set

Published on 05 May 2026 - 6:40

105

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Show that $ F(t) = \int_E f(t + x)d\lambda(x)$ is Borel measurable

Published on 03 May 2026 - 12:03

302

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Equivalent definitions of standard Borel space?

Published on 02 Nov 2019 - 16:12

261

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Proving a vector space contains all Borel-measurable functions

Published on 06 May 2026 - 6:55

82

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Regular measure

Published on 10 May 2026 - 9:24

List Question

Prove that $e^{-x}I(x \geq 0)$ is a measurable function in the Lebesgue measure space given by $(R, \mathcal{B}, \lambda)$

Is my proof of uniform exterior regularity of Lebesgue measure correct?

Existence of increasing sequence of compact sets

On the definition of bounded variation

Any translation invariant Borel measure such that $\mu([0,1))=1$ is identical to the Lebesgue measure

Are $\phi(X^2)$ and $\psi(Y^2)$ always independent where $\phi$ and $\psi$ are Borel-Measurable functions (X,Y are any two RVs)?

Is any continuous functions between Hausdorff spaces measurable wrt. the Borel algebras?

Compact support of measure.

Question on Borel Measurable Functions and Borel Sigma Algebras.

f(X) and f(Y) are identically distributed

Prove that a set is a Borel set

Show that $ F(t) = \int_E f(t + x)d\lambda(x)$ is Borel measurable

Equivalent definitions of standard Borel space?

Proving a vector space contains all Borel-measurable functions

Regular measure

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