Assumptions: f:[a,b]\to\mathbb{R} is some measurable function, and M is some constant. We assume that the function has the following property:
[x,x']\subset [a,b]\quad\implies\quad |f(x')-f(x)|\leq M(x'-x)
The claim: The function also has the property
m^*(f([a,b]))\leq M(b-a)
I'm not...