Question: Suppose that f : [0, 1] [a, b] is integrable on [0, 1]. Assume that ef(x) and |f(x)|p are integrable for all 0 a)

Suppose that f : [0, 1] †’ [a, b] is integrable on [0, 1]. Assume that ef(x) and |f(x)|p are integrable for all 0 a) Prove that
1/r lo fx) dx (lisordx If(x)| dx dx and If(x)l

for all 0 b) If 0

Suppose that f : [0, 1] †’ [a, b] is

c) State and prove analogues of these results for improper integrals.

1/r lo fx) dx (lisordx If(x)| dx dx and If(x)l" dx

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