This isn't a homework question. My adviser has me studying basic analysis and has lately pushed me towards the following question:(adsbygoogle = window.adsbygoogle || []).push({});

"Let f be any continuous function. Can we prove that there exists a SEQUENCE of step functions that converges UNIFORMLY to f?"

I have noticed this idea is important to Riemann integrability but I can't seem to prove this. Or notice why the idea of uniform convergence is so key.

Any help? Thank you

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# Riemann Integrability Question

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