Measure Extension and Decomposition

Abstract

Outer measure, Caratheodory extension, Lebesgue measure, shift and rotation invariance, Hahn and Jordan decompositions, Lebesgue decomposition and differentiation, Radon–Nikodym theorem, Lebesgue–Stieltjes measures, finite-variation functions, signed measures, atomic decomposition, factorial measures, right and left continuity, absolutely continuous and singular functions, Riesz representation.