Contents of Measure Theory, by D.H.Fremlin

Chapter 23: The Radon-Nikodým theorem

231 Countably additive functionals
Additive and countably additive functionals; Jordan and Hahn decompositions.

232 The Radon-Nikodým theorem
Absolutely and truly continuous additive functionals; truly continuous functionals are indefinite integrals; *the Lebesgue decomposition of a countably additive functional.

233 Conditional expectations
σ-subalgebras; conditional expectations of integrable functions; convex functions; Jensen's inequality.

234 Operations on measures
Inverse-measure-preserving functions; image measures; sums of measures; indefinite-integral measures; ordering of measures.

235 Measurable transformations
The formula ∫g(y)ν(dy)=∫J(x)g(φ(x))μ(dx); detailed conditions of applicability; inverse-measure-preserving functions; the image measure catastrophe; using the Radon-Nikodým theorem.

TeX, PDF, ro-PDF (results-only version).
Return to contents page.

Revised 19.1.16