- #1
quantarb
- 1
- 0
Homework Statement
I am trying to prove that if f is continuous almost everywhere on [a,b], and if g is cont a.e. on [c,d], with
f[a,b] contained in [c,d], then g composite f is cont. a.e.
The Attempt at a Solution
------
Originally, my proof went something like this:
f is cont. a.e. implies f is Riemann integrable
g is cont. a.e. implies g is Riemann integrable
since f and g are Riemann integrable, g composite f is Riemann integrable (*)
A Riemann integrable function is cont. a.e., thus g composite f is cont. a.e.
-------
I was satisfied with this until I realized (*) might not be true, as I couldn't prove it as a Lemma.
Also, I am a newby to this forum - does anyone know if there is a way to LaTex my input?
Thanks