Tagged Questions

130 views

Absolute continuity of probabilities on Polish spaces and open sets.

On a polish space $\mathcal{X}$ i consider two Borel probabilities $P$ and $Q$ such that for any open set $E$ of $\mathcal{X}$ we have : $P(E) =0$ implies $Q(E)=0$. Does this imply that $Q$ is ...
412 views

Is the set of the absolutely continuous functions a Borel set of the space of the continuous functions ?

Does anyone knows whether the set of the absolutely functions $F :[0,1]\to \mathbb{R}^d$ of the form $$F(t)= a + \int_0^tf(s) ds$$ where $f$ is an integrable function is a Borel set of the Banach ...
558 views

Convergence of probability measure and the *-weak convergence ?

Given a Polish space X, I note $C_b(X)$ the set of the continuous bounded functions with the norm of the uniform convergence, and and $(C_b(X))^\star$ its topological dual with the $*-$weak ...
284 views

Probability that a random distance function is metric

Take a random $n \times n$ nonnegative symmetric matrix $D$ with zero diagonal. What is the probability that it is an abstract distance matrix, i.e. satisfies $D_{xy}+D_{yz} \geq D_{xz}$ for all index ...
Defining measures over frames in place of $\sigma$-algebras
Normally measures and probability spaces are defined over $\sigma$-algebras. I was wondering what would happen if one tries to define it over frames in place of $\sigma$-algebras? (i.e. complements do ...
Does anyone know an example of non-separable $L^1$ of a probability space?
It is easy to give examples of non-separable $L^p$ spaces by considering a measure on a big space. If one adds the condition that the space has to have total measure 1, the problem is not as easy. ...