hw1.pdf - Modern Analysis 2 Homework 1 1 Let f[0 1 R be...

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Modern Analysis 2 Homework 1 1. Let f : [0 , 1] R be defined as follows: if the rational t is m/n in lowest terms then f ( t ) = 1 /n ; if t is irrational then f ( t ) = 0 (define f (0) ad lib ). Prove that f is Riemann-integrable on [0 , 1] and that R 1 0 f = 0. 2. Let 1 A : [0 , 1] R be the indicator function of the set
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