Let $f\colon \mathbb R\to (0,\infty)$ be a function taking positive values. Does there exist a Borel measurable function $g\colon \mathbb R\to (0,\infty)$ taking positive values as well such that $g(x)\leq f(x)$ for all $x\in\mathbb R$?
Existence of a Borel measurable function
Mario
- 13
- 2