Trevor Leslie : Some basic properties of Radon measures

Posted by Trevor Leslie , part of the Graduate Analysis Seminar.

At

March 28, 2016, 2 p.m.

In

SEO 612

Abstract

With the aim of understanding the dual space of $C_0(X)$, the continuous functions on a (locally compact Hausdorff) space $X$ which vanish at infinity, we introduce Radon measures and prove that there is a natural bijection between the set of positive linear functionals on $C_c(X)$ (the space of compactly supported continuous functions on $X$) and the space of Radon measures on $X$.