Chapter 34: Liftings
341
The lifting theorem
Liftings and lower densities; strictly localizable spaces have lower
densities; construction of a lifting from a density; complete
strictly localizable spaces have liftings; liftings and Stone spaces.
342
Compact measure spaces
Inner regular measures; compact classes; compact and locally
compact measures; perfect measures.
343
Realization of homomorphisms
Representing homomorphisms between measure algebras by functions;
possible when target measure space is locally compact; countably
separated measures and uniqueness of representing functions; the
split interval; perfect measures.
344
Realization of automorphisms
Simultaneously representing groups of automorphisms of measure
algebras by functions -- Stone spaces, countably separated measure
spaces, measures on {0,1}I; characterization of Lebesgue
measure as a measure space; strong homogeneity of usual measure on
{0,1}I.
345
Translation-invariant liftings
Translation-invariant liftings on Rr and {0,1}I; there
is no t.-i. Borel lifting on R.
346
Consistent liftings
Liftings of product measures which respect the product structure;
translation-invariant liftings on {0,1}I; products of Maharam-type-homogeneous
probability spaces; lower densities respecting product structures;
consistent liftings; the Stone space of Lebesgue measure.
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