I read the textbook and it states that "with the Riemann step functions $f:[a,b] \rightarrow \mathbb{R}$, the Lebesgue integral and the Riemann integral coincide" Can someone give some hints to this statement?
2026-03-31 14:13:09.1774966389
Riemann integral and Lebesgue integral coincide for step functions
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Hint:
Write down by definition what a step function looks like and then calculate by definition the Riemann integral and Lebesgue integral on $[a,b]$ respectively.
As a concrete example, can you calculate $$ \int_0^1f(x)\ dx\quad\textrm{and }\int_{[0,1]}f(x)\ dx $$ where $f(x)=1_{[0,.5]}$?