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; ω_{1}-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 *C _{b}*(

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; **N ^{c}** is not Borel-measure-compact; the
Sorgenfrey line;

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Revised 24.8.15