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
Fun book indeed!
Your first example you won't typically run into until an introductory measure theory course.
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.