# Multiplication of simple function looks like?

I was wondering what does the multiplication of two Lebesgue integrable simple functions look like. Assume integral of a function f is defined as

• The product of two measurable simple functions is a measurable simple function. – MPW May 23 at 11:26

If $$\mathbb{1}_A$$ stands for the indicatrice function of the measurable set $$A$$, that is takes values $$1$$ and $$0$$ and is $$1$$ exactly on $$A$$, then
\begin{align} \mathbb{1}_A \times \mathbb{1}_B = \mathbb{1}_{A\cap B} \end{align}