Show that I E R*[a, b] with integral L if and only if for every E > 0 there exists a

Chapter 10, Problem 6

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Show that I E R*[a, b] with integral L if and only if for every E > 0 there exists a gauge Yeon [a, b] such that ifP = {([xi_., Xi]' ti)}7=. is any tagged partition such that 0 < xi - xi_. :::y/ti) for i = 1, ..., n, then IS(f; p) - LI < E. (This provides an alternate-but equivalentwayof defining the generalized Riemann integral.)

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