Unique nonnegative radon measure

Reference no: EM13990828

Recall that a Radon measure on R is a function µ into R, defined on all bounded Borel sets and countably additive on the Borel subsets of any fixed bounded interval. Show that for any convex function f on an open interval U ⊂ R, there is a unique nonnegative Radon measure µ such that f 1(y+) - f 1(x +) = µ((x, y]) and f 1(y-) - f 1(x -) = µ([x, y)) for all x y in U.

Reference no: EM13990828

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