List questions from borel-measures

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interpret a borel-set definition of a random variable to a 101 probability theory definition

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Product of $\sigma$-algebras Axler MIRA 5A.1

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Borel measure $\mu$ with $f'(a)$ an integral of $f$ w.r.t $\mu$

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Regular Borel measures

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A measure on a borel $\sigma$-algebra of $\mathbb{R}$ is translation invariant

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Borel measure on a compact metric space

Published on 08 Jan 2023 - 20:49

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Is $x \mapsto \mu( \text{supp}f_x)$ continuous?

Published on 10 Jan 2023 - 13:49

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Question about a finite Borel Measure

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Let $X$ be locally compact and separable. Can we replace $C_c(X)$ with the space of Lipschitz functions with compact supports in weak convergence?

Published on 15 Jan 2023 - 13:05

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A Half Partition of Borel Sets will Give Half the Borel Measure

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Prove that there are 2^c measurable sets in every interval.

Published on 23 Jan 2023 - 11:45

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Showing that the Fourier transform of a finite Borel measure $\mu$ with compact support is Lipschitz continuous function in $\mathbb{R}^n$

Published on 24 Jan 2023 - 10:13

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Why does $|\hat{\mu}(x)|\leq|x|^{-s/2} \implies \int_{\mathbb{R}^n}|\hat{\mu}(x)|^2|x|^{s-n}dx<\infty$ for the Fourier transform of a measure $\mu$

Published on 25 Jan 2023 - 18:00

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Exercise on Levy measure

interpret a borel-set definition of a random variable to a 101 probability theory definition

Product of $\sigma$-algebras Axler MIRA 5A.1

Borel measure $\mu$ with $f'(a)$ an integral of $f$ w.r.t $\mu$

Regular Borel measures

A measure on a borel $\sigma$-algebra of $\mathbb{R}$ is translation invariant

Borel measure on a compact metric space

Is $x \mapsto \mu( \text{supp}f_x)$ continuous?

Question about a finite Borel Measure

Let $X$ be locally compact and separable. Can we replace $C_c(X)$ with the space of Lipschitz functions with compact supports in weak convergence?

A Half Partition of Borel Sets will Give Half the Borel Measure

Prove that there are 2^c measurable sets in every interval.

Showing that the Fourier transform of a finite Borel measure $\mu$ with compact support is Lipschitz continuous function in $\mathbb{R}^n$

Why does $|\hat{\mu}(x)|\leq|x|^{-s/2} \implies \int_{\mathbb{R}^n}|\hat{\mu}(x)|^2|x|^{s-n}dx<\infty$ for the Fourier transform of a measure $\mu$

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