Index
Adjoint Operator, 10
AF-algebra, 13
Algebra
AF, 14
C \ 10
maximal abelian, 10
von Neumann, 10
Allowed
map, 56
word, 56
Alphabet, 55
Amenable
equivalence relation, 15
group, 15
group action, 15
Ample group, 13
Araki, 22
Asymptotically invariant sequence, 38
trivial, 38
Automorphism
of a measure Space
conservative, 6
induced, 5
measure preserving, 5
nonsingular, 4
of an equivalence relation, 4, 31
inner, 4
Belinskaya, 31
Bernoulli action, 36
Beta function (of a Markov shift), 23
Borel
equivalence relation, 4
set, 3
space, 3
C*-algebra, 10
of an equivalence relation, 12
of a Markov shift, 12
Cellular automaton, 61
Central
limit theorem, 21
sequence, 38
Chain recurrence, 46
Coboundary
of an equivalence relation, 18
of a group action, 28
Cocycle, 18
bounded, 29
cohomologous, 18
index, 24
induced, 21
Information, 41
of a group action, 28
of a Markov shift, 41
recurrent, 20
transient, 20
Cohomologous, 18, 28
Cohomology, 18
group, 18
invariant, 19
lemma, 23
Commutant (of a self-adjoint set of
Operators), 10
Completely positive entropy, 62
Conditional expectation, 17
Conjugacy
of automorphisms of an equivalence
relation, 31
outer, 32
of group actions, 5
of Markov shifts, 68
algebraic, 68
metric, 7
topological, 68
Connes, 14, 16, 23, 32, 35,40
Containment of the trivial
representation, 39
Continued fraction
expansion, 10
transformation, 9
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