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Let $T$ be a ergodic automorphism of a non-atomic Lebesgue probability space $(X, \mathcal{A}, \mu)$. The celebrated Rokhlin tower lemma says that given an integer $n>0$ and $0 < \epsilon < 1$, there …

For a result of a somewhat similar type, check the paper "Rate of approximation of minimizing measures" by Bressaud and Quas, 2007, especially Theorem 4. In their case the dynamics is a subshift of fi …

Your set consists exactly of weak coboundaries plus constants. A function $f\in C(X)$ is called a coboundary if $f = h \circ T - h$ for some $h\in C(X)$. A function is called a weak coboundary if it …

The question has already been answered, so let me just complement what has been said. The book which I find most accessible is Lang's Fundamentals of Diff. Geom. (it was recommended to me by Karlsso …

My "answer" is just a (still another) reformulation of Ian's. Given two subspaces $V$, $W \subset \mathbb{R}^n$ with the same dimension, define their distance as: $$ d(V,W):= \inf_J \| J - i_V\| $$ w …

It is known that minimality does not imply unique ergodicity (Furstenberg example). I ask whether the implication holds in following particular situation: Suppose $X$ is a compact space, $f:X \to …