Category:Pointwise Product of Simple Functions is Simple Function

This category contains pages concerning Pointwise Product of Simple Functions is Simple Function:

Let $\struct {X, \Sigma}$ be a measurable space.

Let $f, g : X \to \R$ be simple functions.

Then $f \cdot g: X \to \R, \map {\paren {f \cdot g} } x := \map f x \cdot \map g x$ is also a simple function.