# What is a deterministic, non-negative, and Borel-measurable function?

May I know the intuitive understanding of a deterministic, non-negative, and Borel-measurable function?

Especially, I am not sure what the 'deterministic' and 'Borel-measurable' functions are.

Thank you.

• Do you know what a borel space is? – Q the Platypus Jan 30 '17 at 0:36

In other words if $f : \mathbb{R}^k \to \mathbb{R}$ is a borel measurable function then for every interval $\Delta$, $f^{-1}[\Delta]$ is a borel subset of $\mathbb{R}^k$.