All Questions

Let $b\in \mathbb{R}\neq 0$, and consider the translation operators: $$ \begin{align} T_b:C(\mathbb{R}) & \rightarrow C(\mathbb{R})\\ f &\mapsto f(\cdot + b). \end{align} $$ *Are there known ...

Musielak-Orlicz spaces provide a generalization of the usual $L^p$ spaces on $(\mathbb{R},\mathcal{B}(\mathbb{R}))$ to spaces of functions for which the Luxemburg norm $$ \|f\|_M:=\inf\left\{\lambda &...

If $f_n (\omega) = \sum_{i=1}^n f_1 (T^i \omega)$ and $T$ is an ergodic action with respect to the measure $\mu$ then it is know as Birkhoff's theorem that $$ \lim_{n \rightarrow \infty} \frac{f_n}{...