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