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}>ω_{1}.

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**,
cov** N**, FN(

533
Special topics

add** N** and (quasi-)Radon measures of countable Maharam type;
uniformly regular measures; when

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(** S**mz), add(

535
Liftings

Liftings of non-complete measure spaces; Baire liftings for usual
measures on {0,1}^{κ}; tightly ω_{1}-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