A function of bounded variation on an interval is differentiable a.e.?

Question

I am wondering is a function of bounded variation on an interval is differentiable a.e? If it is true, how to prove it? Thanks!

Related: Bounded variation, difference of two increasing functions — robjohn, Apr 07 '17 at 15:49

score 3 · Answer 1 · answered Apr 07 '17 at 15:38

3

A function of bounded variation can be written as the difference of two increasing functions. Increasing functions are differentiable a.e. QED

answered Apr 07 '17 at 15:38

robjohn

1 Answers1