No, it's doable at the level of
Rudin's Principles:
He shows that a function is
Riemann integrable if and only
if it is continuous everywhere
except on a set of measure 0.
For the definition of measure 0,
he gives that quickly, and don't
really need a course in measure
theory. Besides a course in
measure theory likes just to
f'get about Riemann integration,
and thankfully so.
Agree, it's do-able with baby Rudin. But as I recall it's a typical example used (early) in measure theory, not so much intro analysis. Hence "typical".
Comments
No, it's doable at the level of Rudin's Principles: He shows that a function is Riemann integrable if and only if it is continuous everywhere except on a set of measure 0.
For the definition of measure 0, he gives that quickly, and don't really need a course in measure theory. Besides a course in measure theory likes just to f'get about Riemann integration, and thankfully so.
Agree, it's do-able with baby Rudin. But as I recall it's a typical example used (early) in measure theory, not so much intro analysis. Hence "typical".
Ymmv, of course.