Week 10 – Riemann Integrability of the Cantor Function

This week, in addition to the assigned reading, I developed a more comprehensive proof of why the Cantor function is Riemann integrable. This involves proving that f_n(x) is uniformly continuous, and that f_n(x) converges uniformly to the Cantor function. The only point of confusion I had was at the end of the proof that f_n(x) converges uniformly, at the end of the section where I prove the induction step by demonstrating that |f_n+p(x) – f_n(x)| < epsilon implies that |f_n+p+1(x) – f_n(x)| < epsilon. I felt like the argument could be made stronger, but I was not exactly sure the best way to go about it.