Steffensen's inequality proof
Submitted by MSA on Sat, 12/10/2011 - 17:04.
Johan Frederik Steffensen (1873–1961)
ƒ : [a, b] → R is a non-negative, monotonically decreasing, integrable function and
g:[a, b] →[0, 1] is another integrable function, then:
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where
First we see that and
. We have
and
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so
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We have also
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take and
and
so
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That proof the inequality.