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 …

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 AS …

In their paper titled "The Classification of Hypersmooth Borel Equivalence Relations" Alexander Kechris and Alain Louveau quote the following (Theorem 5.2 in the article) as "Harri …

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 $G_{\delta\sigma}$ …

This is a simple doubt of mine about the basics of measure theory, which should be easy for the logicians to answer. The example I know of non Borel sets would be a Hamel basis, w …

Is the following generalised compactness property of Borel sets in a Polish space consistent with ZFC? (*) Let $\mathcal{B}$ be a family of $\aleph_1$-many Borel sets. If $\bigca …

Hi, I want to write a proof that relies on the fact that: There are Borel Sets $A$ and $B$ contained in $\mathbb{R}$ such that $A \cap B = \emptyset$ and $\lambda(A \cap (x,y)) …

Hello, consider the following theorem. Is it trivial? Is it interesting? Is it worth including in a paper if I can prove it in 1 line as a corollary? Theorem: Suppose $n>0$ is …

Hello This should be easy to prove but i have no idea how to do it: If $X \subseteq \mathbb{R}^2$ is borel then $f(X)$ is borel where $f(x,y) = x$ Thanks Tobias

I'm trying to do due diligence and determine whether this is known, trivial, original, etc. I have a proof of: Theorem: If $S\subseteq \mathbb{N}^{\mathbb{N}}$ then $S=X\cup Y$ f …