$\newcommand{\vp}{\varphi}$$\newcommand{\dmux}{\,\text d\mu(x)}$$\newcommand{\dmu}{\,\text d\mu}$$\newcommand{\E}{\operatorname{E}}$Let $\mu$ be a probability measure on $(\mathbb R, \mathbb B)$ where $\mathbb B$ is the Borel $\sigma$-algebra…
$\newcommand{\e}{\varepsilon}$In this post I’ll be exploring non-integer bases and the “natural numbers” they represent. I say “natural numbers” because the…