Staircase function/Sum product maximum minimum/Exercise

Let

$f,g\colon [a,b]\longrightarrow \mathbb {R}$

be two staircase functions. Show that also

1. ${}f+g$,
2. ${}f\cdot g$,
3. ${}{\max {\left(f,g\right)}}$,
4. ${}{\min {\left(f,g\right)}}$,

are staircase function.

Create a solution