Let {rl, r2, . . . , rn . . .} be an enumeration of the rational numbers in I := [0, 1]
Chapter 8, Problem 16(choose chapter or problem)
Let {rl, r2, . . . , rn . . .} be an enumeration of the rational numbers in I := [0, 1], and let In :I -+ JRbe definedto be 1 if x = rl, .. " rn and equal to 0 otherwise. Show that In is Riemannintegrable for each n E N, that II (x) ::s 12 (x) ::s .. . ::s In (x) ::s .. . and that I (x) := lim(ln (xis the Dirichlet function, which is not Riemann integrable on [0, 1].
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