Contents of Measure Theory, by D.H.Fremlin

Chapter 53: Topologies and measures III

531 Maharam types of Radon measures
Topological and measure-theoretic cardinal functions; the set MahR(X) of Maharam types of homogeneous Radon measures on X; MahR(X), precalibers and continuous surjections onto [0,1]κ; MahR(X) and χ(X); a perfectly normal hereditarily separable space under CH; when mK1.

532 Completion regular measures on {0,1}I
The set MahcrR(X) of Maharam types of homogeneous completion regular Radon measures on X; products of quasi-dyadic spaces; convexity of the relation `λ∈MahcrR({0,1}κ)'; the measure algebra of {0,1}λ; d, covN, FN(PN), addN and the case λ=ω; □, Chang's conjecture and the case cfλ=ω.

533 Special topics
addN and (quasi-)Radon measures of countable Maharam type; uniformly regular measures; when Rκ is measure-compact.

534 Hausdorff measures and strong measure zero
Cardinal functions of Hausdorff measures; strong measure zero in uniform spaces; Rothberger's property; σ-compact groups; non(Smz), add(Smz); Smz-equivalence; uncountable sets with strong measure zero.

535 Liftings
Liftings of non-complete measure spaces; Baire liftings for usual measures on {0,1}κ; tightly ω1-filtered measure algebras; Mokobodzki's theorems; strong Borel liftings; Borel liftings for Radon measures on metrizable spaces; linear liftings; problems.

536 Alexandra Bellow's problem
The problem; consequences of a negative solution.

537 Sierpinski sets, shrinking numbers and strong Fubini theorems
Sierpinski and strongly Sierpinski sets; entangled totally ordered sets; non-ccc products; scalarly measurable functions; repeated integrals of separately measurable functions; changing the order of integration in multiply repeated integrals; shr+, cov and repeated upper and lower integrals.

538 Filters and limits
Filters on N; the Rudin-Keisler ordering; products and iterated products; Ramsey ultrafilters; measure-centering ultrafilters; extending perfect measures with measure-centering ultrafilters; Benedikt's theorem; measure-converging filters; the Fatou property; medial functionals and limits.

539 Maharam submeasures
Maharam algebras; Maharam-algebra topology, pre-ordered set of partitions of unity, weak distributivity, π-weight, centering number, precalibers; null ideals of Maharam submeasures; splitting reals; Quickert's ideal; Todorcevic's p-ideal dichotomy; a consistent characterization of Maharam algebras; Souslin algebras; reflection principles; exhaustivity rank, Maharam submeasure rank.

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Revised 30.8.14