Suppose that f : [0, ) [0, ) is integrable on every closed interval [a,b]

Suppose that f : [0, ˆž) †’ [0, ˆž) is integrable on every closed interval [a,b] Š‚ [0, ˆž). If

then there is a function g : [0, ˆž) †’ [0, ˆž) such that F(x) = ˆ«xg(x) f(y)dy for all x ˆˆ [0, ˆž).

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F(x) := | e-r f(y) dy, x ε 10, 00), 0