相关论文: A new ergodic proof of a theorem of W. Veech

The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.

An technically interesting proof of a known theorem.

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…

We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the…

The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.

We present a short proof of Szemer\'edi's Theorem using a dynamical system enriched by ideas from model theory. The resulting proof contains features reminiscent of proofs based on both ergodic theory and on hypergraph regularity.

We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.

This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.

We give a new proof of Lucas' Theorem in elementary number theory.

Almost uniform version of noncommutative Wiener-Wintner ergodic theorem and its extension to Besicovitch weights are proved.

We give a new simpler proof of a theorem of Jayne and Rogers.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We will present several examples in which ideas from ergodic theory can be useful to study some problems in arithmetic and algebraic geometry.

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

Recently, T. Tao gave a finitary proof a convergence theorem for multiple averages with several commuting transformations and soon later, T. Austin gave an ergodic proof of the same result. Although we give here one more proof of the same…

The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…

We present a new, elementary, dynamical proof of the prime number theorem.

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.