# 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 ...
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### 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 ...
552 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 ...
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### Is $C^{\infty}[0,1]$ or $S$ separable?

I want to know if $C^{\infty}[0,1]$ or $S$ (Schwartz function space) is separable. Can somebody offer me some results or references? Thank you!
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### Continuity of multiplicative character

Let $G$ be a discrete group and $\beta (G)$ denote the Stone-Cech compactification of $G$, a right topological semigroup. By a multiplicative character, I mean a mapping that preserves multiplication ...
351 views

### Topological proprieties of Specmax(A)

Hello, We consider $A=C_{b}(X)$ the ring of continous bounded fonction on a completely regular space $X$, SpecMax(A) the set of maximal ideal of $A$ with the zariski topology. We know that there is ...
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### Is the set of real-valued lower semi-continuous functions measurable in epigraph topology (= topology of Gamma convergence)?

Let LSC = LSC([0,1]) be the set of non-negative, lower semi-continuous functions on the unit interval which take values in $\mathbb{R}_+ \cup \{\infty\}$. We use epigraph topology on LSC, i.e. a ...
Let $X$ be a real Banach space. For a continuous (not necessarily linear) function $g:X \to \mathbb{R}$ and a family $\mathcal{F} \subseteq X^*$, we´ll say that $\mathcal{F}$ determines $g$ if ...