# Tagged Questions

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### Topology on the space of Borel measures

Let $B$ be the set of all measures $\phi$ of $\mathbf{R}^{n}$ such that every open set is $\phi$-measurable (sometimes these measures are called Borel measures). Note the measures in $B$ are ...
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### A question about Borel sets on the unit interval

It is known that each non-decreasing continuous function $\phi$ induces a $\sigma$-additive measure $d\phi$ such that $\int_0^1 f(x) d\phi(x)$ exists for every bounded real-valued Baire function $f$. ...
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### Borel subsets of Polish groups

Suppose that I have a polish group $G$ and two subsets $A$ and $B$ of $G$ such that: $A$ is open in $G$ and $B$ is closed in $G,$ from this, can I conclude that $AB$ is a Borel subset of $G$? if not, ...
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### Analytic equivalence relations whose classes are sometimes Borel

There are analytic equivalence relations for which the statement "All classes are Borel" is independent of $ZFC$. In all the examples I know about, the classes are non Borel in $L$ or $L[z]$ for some ...
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### When do Borel $\sigma$-algebras generated by the total variation norm and the weak* topology coincide?

I am almost certain that I read somewhere that the following is true, but I cannot seem to locate the reference. I would be most appreciative if someone could point me to a reference. The result was ...
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### Best introduction to probability spaces, convergence, spectral analysis

I'm not sure if this stuff all falls under what most would just term "probability", but I'm researching applied macroeconomics and need to get a handle on the following concepts ASAP: probability ...
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### A G-delta-sigma that is not F-sigma?

A subset of $\mathbb{R}^n$ is $G_\delta$ if it is the intersection of countably many open sets $F_\sigma$ if it is the union of countably many closed sets $G_{\delta\sigma}$ if it is the union ...