Chapter 39: Measurable algebras
Measurable algebras; strictly positive additive functionals and weak (σ,∞)-distributivity; additive functionals subordinate to or dominating a given functional; intersection numbers; existence of strictly positive additive functionals.
Submeasures; exhaustive, uniformly exhaustive and Maharam submeasures; the Kalton-Roberts theorem (a strictly positive uniformly exhaustive submeasure provides a strictly positive additive functional); strictly positive submeasures, associated metrics and metric completions of algebras; products of submeasures.
Maharam submeasures; Maharam algebras; topologies on Boolean algebras; order-sequential topologies; characterizations of Maharam algebras.
PV norms; exhaustive submeasures which are not uniformly exhaustive; non-measurable Maharam algebras; control measures.
Full local semigroups; τ-equidecomposability; fully non-paradoxical subgroups of Aut(A); ⎣b:a⎦ and ⌈b:a⌉; invariant additive functions from A to L∞(C), where C is the fixed-point subalgebra of a group; invariant additive functionals and measures; ergodic fully non-paradoxical groups.
The Hajian-Ito theorem
Invariant measures on measurable algebras; weakly wandering elements.
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