Date: sunday 31 may '09, at 12:00 pm Department Room

Speaker: Prof. B.Bojarski Academy of Science, Poland

Title: Differentiability of measurable functions and Whitney-Luzin type structure theorems.

Abstract: In the lecture I shall introduce the simple concept of k-quasi smooth functions, k-integer >=0, on arbitrary measurable subset of R(n) and show how this concepts unifies the ideas of H.Whitney on smooth functions on arbitrary closed subsets of R(n) with the Luzin-Egorov-Denjoy 'a structure theorems for measurable functions. In the lectures only very classical concepts of analysis are used. Applications to Sobolev spaces, potential theory, harmonic analysis will be mentioned very briefly. Lecture will be organized for very broad audience.