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Step Functions and Riemann Integrals

If f is defined on [a,b] and and are, respectively, a nondecreasing and a nonincreasing sequence of step functions such that for all k and all and for almost all , show that f is Riemann integrable on [a,b].

Notes from section of book below:

Section 5 Notes:

Theorem 5.1 If f is Riemann integrable on [a,b], then f is continuous almost everwhere on [a,b].

Theorem 5.2 If f is bounded and continuous almost everywhere on [a,b], then f is Riemann integrable on [a,b].

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