A Marginal Ergodic Theorem

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Individual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Beardwood–halton–hammersley Theorem for Stationary Ergodic Sequences: a Counterexample by Alessandro Arlotto

We construct a stationary ergodic process X1,X2, . . . such that each Xt has the uniform distribution on the unit square and the length Ln of the shortest path through the points X1,X2, . . . ,Xn is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton, and Hammersley [Proc. Cambridge Philos. Soc. 55 (1959) 299–327] theorem does not extend f...

Beardwood-halton-hammersley Theorem for Stationary Ergodic Sequences: a Counterexample

We construct a stationary ergodic process X1, X2, . . . such that each Xt has the uniform distribution on the unit square and the length Ln of the shortest path through the points X1, X2, . . . , Xn is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton and Hammersley theorem does not extend from the case of independent uniformly distribut...

ON LOCAL HUDETZ g-ENTROPY

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.