On an inequality for convex functions

H. D. Brunk
1956 Proceedings of the American Mathematical Society  
4) f f[Xit)]dGit)^f\ f Xit)dGit)] J [o,6] LV [a,b] J 2. A nondecreasing approximant to a function. Let Xit) be nondecreasing on the interval [a, b], and let Git) he measurable with respect to the Lebesgue-Stieltjes measure induced by Xit); in particular G will have this property if it is Borel measurable, in particular, J la,b] LV[a,f>] J for every continuous convex f is that G* be a distribution function on [a, b], that is, that G*(a)=0, G*(b) = 1. One has immediately, on applying the theorem
more » ... plying the theorem to f-c<¡> for appropriate constants c,
doi:10.1090/s0002-9939-1956-0081371-9 fatcat:7pddnmqp7vgyjpse7r4avkfiqy