MathOverflow

Setup: Katrin Wehrheim and I recently needed the following result:
Suppose that $\Gamma$ and $\Omega$ are normed vector spaces, and that $F\colon V_\Gamma \to \Omega$ is a uniformly-$C^\ell$ map ($\ell\geq0$), for $V_\Gamma \subset \Gamma$ an open subset. Then:...

I'm studying Billingsley's convergence of probability measures, and wondering why the definition of "Relative compactness of a family of probability measures" reasonable.
In the discussion the set $X$ is always assumed to be a metric space, and let $\mathcal{P}(X)$ be the space of all Borel probability measures on $X$ equipped with weak convergence topology....

Does Tao's stabilisation theorem (Acta Math 2019, Theorem 1.3) apply when the initial condition is restricted to odd multiples of 3 in residue classes {3,9,15} mod 24?

Let $X$ be a countable state space, let $F:X\to X$ be a deterministic map, and let $R\subseteq X\times X$ be the corresponding backward relation, so that$$F(x)=y \iff x\in R(y).$$
Thus the forward and backward orbit descriptions represent the same orbit structure, read in opposite directions....