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Zaharopol R. — Invariant Probabilities of Markov-Feller Operators and Their Supports |
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Предметный указатель |
-equicontinuous Markov — Feller pair (S, T) (or operator S) 76
-equicontinuous Markov — Feller pair (S, T) (or operator S) 76
decomposition 38
-compact topological space 6
(S, T)-ergodic measure 18
Abstract -space 29
AL-space 29
Almost everywhere (a.e.) convergence 20
Alphabet 48
AM-space 29
AM-space, with unit 29
Archimedean Riesz space 31
Attractive probability 18
Banach lattice 29
Banach limit 25
Band 31
Band; generated by a subset of a Riesz space 31
Begins with (the word) w (about a sequence of letters of some alphabet) 49
Bounded sequence of real-valued functions 35
Characteristic function of a word 49
Common (absolute) maximum 67
Contraction 3 20 30
DGP condition 61
DGP-A condition 70
Dirac measure 3
Disjoint complement of a nonempty subset A of a Riesz space E 31
Dissipative Markov — Feller pair 22
Dissipative part of X (generated by a Markov — Feller pair) 22
Distance from a point to a subset A of X 19
Dominant generic point 61
Dominant generic point for a subset A of X 70
e.m.d.s. property 80
Elementary measure 39
Equicontinuous family (or sequence) on the compact subsets of a metric space 33
Equicontinuous family of real-valued functions 32
Equicontinuous family of real-valued functions on a subset of a metric space 32
Equicontinuous sequence of real-valued functions 32
Equicontinuous sequence of real-valued functions, on a subset of a metric space 32
Ergodic measure 18
Feller operator 3
Foias operator 54
Generic point (for a Markov — Feller pair) 61
Ideal 30
Invariant (sub)set 14
Invariant probability 17
Invariant set (with respect to P) 18
Isometric and order isomorphic (about two Banach lattices) 30
Letter (of an alphabet) 48
Lexicographical order 29
Linear lattice 28
Lipschitz function 28
Logistic map 15
Markov operator 3 20 30
Markov operator, generated (or defined) by a transition probability 5
Markov pair (defined by a transition probability P) 43
Markov — Feller kernel 53
Markov — Feller operator 3
Markov — Feller pair 3
Markov — Feller pair, induced by a continuous function 13
Markov — Feller pair, induced by a kernel 54
Markov — Feller pair, induced by a probability and a kernel k 54
Markov — Feller pair, induced by a transition probability (in general metric spaces (not necessarily locally compact, or separable) 43
Minimal Markov — Feller pair (or operator) 51
| Minimal set (with respect to a continuous function) 15
Minimal symbolic flow 15
Monotone class of subsets of a set X 11
Nonsingular (generic) point 61
Orbit of an element under the action of a Markov — Feller operator or pair 44
Orbit-closure of an element under the action of a Markov — Feller operator or pair 44
Order ideal 30
Order isomorphic (about two Banach lattices) 30; see “Isometric and order isomorphic”
Order unit (strong) 29
Ordered vector space 28
P-invariant set 18
Positive element, 2 28
Positive element, in the topological dual E' of a Banach lattice E 30
Positive operator 3 20 30
Quadratic map 15
Quasi-regular point (for a Markov — Feller pair) 61
Regular word (for a sequence of letters of an alphabet) 49
Riesz space 28
Ring of subsets of a set X 11
Rotation of the unit circle 14
Second disjoint complement of a nonempty subset A of a Riesz space E 31
Singular (generic) point 61
Standard extension of a measure 18
Starts with (the word) w (about a sequence of letters of some alphabet) 49
Strictly ergodic 18
Strong order unit 29
Strongly regular word (for a sequence of letters of an alphabet) 49
Support of a continuous function 9
Symbolic flow 15
T-ergodic measure 18
T-invariant measure 17
T-invariant probability 17
Tight sequence of probabilities 95
Tight set of probabilities 95
Topological limit of a sequence of subsets of a metric space 24
Topological lower limit of a sequence of subsets of a metric space 24
Topological support of a (continuous) function 9
Topological upper limit of a sequence of subsets of a metric space 24
Topologically connected Markov — Feller pair (or operator) 51
Topologically convergent sequence of subsets of a metric space 24
Transition probability 4
Trivially minimal Markov — Feller pair 53
Uniform convergence (of a sequence of real-valued functions) on the compact subsets of a metric space 34
Uniform limit (of a sequence of real-valued functions) on the compact subsets of a metric space 34
Uniformly -equicontinuous (Markov — Feller pair (S, T) or operator S) 76
Uniformly -equicontinuous (Markov — Feller pair (S, T) or operator S) on the compact subsets of X 76
Uniformly -equicontinuous (Markov — Feller pair (S, T) or operator S) 77
Uniformly Cauchy sequence of real-valued functions on the compact subsets of a metric space 34
Uniformly equicontinuous family (or sequence) on the compact subsets of a metric space 33
Uniformly equicontinuous family of real-valued functions 32
Uniformly equicontinuous family of real-valued functions on a subset of a metric space 32
Uniformly equicontinuous sequence of real-valued functions 32
Uniformly equicontinuous sequence of real-valued functions; on a subset of a metric space 32
Uniquely ergodic 18
Unit (strong order unit of an AM-space) 29
Universal element 60
Universal element with respect to a subset A of X 60
Vector lattice 28
Weak KBBY decomposition 38
Weak* mean ergodic 67
Weak* uniquely mean ergodic 96
Word (of length m with letters in A) 48
x leads to y, , 60
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