Contents of Measure Theory, by D.H.Fremlin

Chapter 43: Topologies and measures II

431 Souslin's operation
The domain of a complete locally determined measure is closed under Souslin's operation; the kernel of a Souslin scheme is approximable from within; Baire-property algebras; ω1-saturated ideals.

432 K-analytic spaces
Topological measures on K-analytic spaces; extensions to Radon measures; expressing Radon measures as images of Radon measures; Choquet capacities.

433 Analytic spaces
Measures on spaces with countable networks; inner regularity of Borel measures; expressing Radon measures as images of Radon measures; measurable and almost continuous functions; the von Neumann-Jankow selection theorem; products; extension of measures on σ-subalgebras; standard Borel spaces.

434 Borel measures
Classification of Borel measures; Radon spaces; universally measurable sets and functions; Borel-measure-compact, Borel-measure-complete and pre-Radon spaces; countable compactness and countable tightness; quasi-dyadic spaces and completion regular measures; first-countable spaces and Borel product measures.

435 Baire measures
Classification of Baire measures; extension of Baire measures to Borel measures (Marík's theorem); measure-compact spaces.

436 Representation of linear functionals
Smooth and sequentially smooth linear functionals; measures and sequentially smooth functionals; Baire measures; sequential spaces and products of Baire measures; quasi-Radon measures and smooth functionals; locally compact spaces and Radon measures.

437 Spaces of measures
Smooth and sequentially smooth duals; signed measures; embedding spaces of measurable functions in the bidual of Cb(X); vague and narrow topologies; product measures; extreme points; uniform tightness; total variation metric, Kantorovich-Rubinshtein metric; invariant probability measures; Prokhorov spaces.

438 Measure-free cardinals
Measure-free cardinals; point-finite families of sets with measurable unions; measurable functions into metrizable spaces; Radon and measure-compact metric spaces; metacompact spaces; hereditarily weakly θ-refinable spaces; when c is measure-free.

439 Examples
Measures on [0,1] not extending to Borel measures; universally negligible sets; Hausdorff measures are rarely semi-finite; a smooth linear functional not expressible as an integral; a first-countable non-Radon space; Baire measures not extending to Borel measures; Nc is not Borel-measure-compact; the Sorgenfrey line; Q is not a Prokhorov space.

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Revised 24.8.15