Exercise 7.3.7

Assume $f:[a,b]\to R$ is integrable.

(a)

Show that if $g$ satisfies $g(x)=f(x)$ for all but a finite number of points in $[a,b]$, then $g$ is integrable as well.

(b)

Find an example to show that $g$ may fail to be integrable if it differs from $f$ at a countable number of points.