Questions related to measures, sigma-algebras, measure spaces, Lebesgue integration and the like.

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4
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1answer
101 views
+150

Representation of a linear functional Lipschitz in total variation

Let $\Omega$ be a Borel space and let $\mathcal P(\Omega)$ be the space of all Borel probability measures on $\Omega$ endowed with the topology of weak convergence. Define the total variation metric ...
2
votes
0answers
101 views
+150

Linear w.r.t. any measure

Let $X$ be a Banach space endowed with a Borel $\sigma$-algebra. How do we call a real-valued Borel function $f$ that satisfies for any Borel probability measure $\mu$ the following formula $$ ...
2
votes
0answers
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+50

Integrating a probability density function that only depends on the norm

I have a probability density function $f$ on $\mathbb{R}^3$ which only depends on the norm of a vector (that is, it takes the same value for $x,y$ if their length is equal). Let me call a region of ...