Chapter 53: Topologies and measures III

531 Maharam types of Radon measures
Topological and measure-theoretic cardinal functions; the set Mah_R(X) of Maharam types of homogeneous Radon measures on X; Mah_R(X), precalibers and continuous surjections onto [0,1]^κ; Mah_R(X) and χ(X); a perfectly normal hereditarily separable space under CH; when m_K>ω₁.

532 Completion regular measures on {0,1}^I
The set Mah_crR(X) of Maharam types of homogeneous completion regular Radon measures on X; products of quasi-dyadic spaces; convexity of the relation `λ∈Mah_crR({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 R^κ is measure-compact.

534 Hausdorff measures, strong measure zero and Rothberger's property
Cardinal functions of Hausdorff measures; strong measure zero in uniform spaces; Rothberger's property in topological spaces; 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; PV norms and Maharam submeasure rank; the set of exhaustive submeasures on a countable atomless Boolean algebra.

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Revised 1.7.2022