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 **R**^{r} 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.

TeX,
PDF,
ro-PDF (results-only version).

Return to contents page.

Revised 23.12.10