Answer to Question #309395 in Real Analysis for Ammulu

Question

Let f : [0, 1] → [0, 1] be the modified Dirichlet function defined as f(x) = if c = " is rational in lowest terms, 0 if r is irrational and let h : [0, 1] → [0, 1] be the function 1 if x is rational, h(x) = 0 if x is irrational Find an integrable function g: [0,1] [0, 1] such that h=gof, thereby showing that the composition of two integrable functions need not be integrable.

Answer 1

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