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In that case the interval [G(b), G(a)] replaces the interval [G(a), G(b)] in the hypotheses regarding f and F , but the change of variable formula...
In that case the interval [G(b), G(a)] replaces the interval [G(a), G(b)] in the hypotheses regarding f and F , but the change of variable formula (38) remains unchanged. Exercise. The assumption that G is increasing over [a, b] in Proposition 3.1 can be weakened to the assumption that G is nondecreasing over [a, b]. Prove this slightly strengthend lemma.