Entropy of transformations of the unit interval
Entropy on effect algebras with Riesz decomposition property II: MV-algebras
We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.
Entropy on effect algebras with the Riesz decomposition property I: Basic properties
We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.
Equality of coarse topologies in inverse transformations
Equations containing locally Henstock-Kurzweil integrable functions
A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.
Équations fonctionnelles, couplages de produits gauches et théorèmes ergodiques pour mesures diagonales
Equicontinuity and Convergence of Measures.
Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem
Equidecomposability of Jordan domains under groups of isometries
Let denote the isometry group of . We prove that if G is a paradoxical subgroup of then there exist G-equidecomposable Jordan domains with piecewise smooth boundaries and having different volumes. On the other hand, we construct a system of Jordan domains with differentiable boundaries and of the same volume such that has the cardinality of the continuum, and for every amenable subgroup G of , the elements of are not G-equidecomposable; moreover, their interiors are not G-equidecomposable...
Equidistribution of small subvarieties of an Abelian variety.
Equilibrium measures for holomorphic endomorphisms of complex projective spaces
Let f: ℙ → ℙ be a holomorphic endomorphism of a complex projective space , k ≥ 1, and let J be the Julia set of f (the topological support of the unique maximal entropy measure). Then there exists a positive number such that if ϕ: J → ℝ is a Hölder continuous function with , then ϕ admits a unique equilibrium state on J. This equilibrium state is equivalent to a fixed point of the normalized dual Perron-Frobenius operator. In addition, the dynamical system is K-mixing, whence ergodic. Proving...
Equilibrium points of random generalized games.
Equilibrium States for ß-Transformations and Related Transformations.
Equipartitioning Common Domains of Non-Atomic Measures.
Équisingularité réelle : nombres de Lelong et images polaires
Equivalence et orthogonalité des mesures aléatoires engendrées par martingales positives homogènes
Equivalent or absolutely continuous probability measures with given marginals
Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.
Equivanishing sequences of mappings
Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems
Equivariant measurable liftings
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to -cocycles for characteristic classes.
Ergodic and Diophantine properties of algorithms of Selmer type