arXiv subjects
Publications and source records attributed to Michel Valadier.
Blurring of a photographic image by a wrong focus can be modeled by convolution. Is inversion a possible answer? This paper adds complements to a foregoing paper discussing convolution-inversion of some measures.
A real random variable admits median(s) and quantiles. These values minimize convex functions on $\mathbb R$. We show by "Convex Analysis" arguments that the function to be minimized is very natural. The relationship with some notions about functions of bounded variation developed by J.J.~Moreau is emphasized.
This is a detailed survey which mainly presents the Pinkham-Feller way. I added some new points to the first version [V2] and I suppressed "Examples" devoted to Gamma, Fréchet and Weibull laws. Theorem 2 is a bit more general (no assumption of density: this answers a question of T. Hill). Section 10 is new and devoted to an argument (Poincaré, Fewster) about the effect of high frequencies oscillations. Maybe many works, many efforts, have been devoted to the study of a sufficient condition of poor value: see Sections 7 and 11. The final Section gives some suggestions.