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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Step Functions and Riemann Integrals are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.