The Riemann Integral Part 3 - Monotone functions are Riemann integrable
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The Riemann Integral Part 3 - Monotone functions are Riemann integrable
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About this listen
This episode is concerned with providing another class of functions that are Riemann integrable. This class will be monotone functions and are neither contained nor are supersets of the step functions or continuous functions we have identified to be Riemann integrable already. The idea of proof for the desired result in the current episode is the construction of tailored step functions smaller and bigger than the monotone function so that the integral of the difference of the constructed functions gets smaller if the maximal distance of the partition points does so.
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