Easy and nearly simultaneous proofs of the Ergodic Theorem and Maximal Ergodic Theorem

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...

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

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...

An L Ergodic Theorem for Sparse Random Subsequences

We prove an L subsequence ergodic theorem for sequences chosen by independent random selector variables, thereby showing the existence of universally L-good sequences nearly as sparse as the set of squares. In the process, we prove that a certain deterministic condition implies a weak maximal inequality for a sequence of l convolution operators (Prop. 3.1).

Discrete Analogues of Singular Radon Transforms

The purpose of this paper is to describe recent results we have obtained in finding discrete analogues of the theory of singular integrals on curves, or more generally of "singular Radon transforms," at least in the translation-invariant case. Our theorems are related to estimates for certain exponential sums that arise in number theory; they are also connected with Bourgain's recent maximal er...