Ergodic Theory and Applications to Additive Number Theory
نویسنده
چکیده
The following lemma follows the standard paradigm of recurrence results in ergodic theory: given a topological space X which satisfies a suitable ’smallness’ condition (e.g. compactness, μ(X) < ∞), and a transformation T : X → X, there exist points of X which satisfy a certain ’almost-periodicity’ condition under the action of T . Lemma 1. Poincare Recurrence Lemma If (X,β, μ, T ) is an m.p.s. and μ(X) < ∞, then ∀B ∈ β such that μ(B) > 0, ∃N ∈ N such that μ(B∩TB) > 0.
منابع مشابه
Additive Combinatorics and Theoretical Computer Science ∗ Luca Trevisan
Additive combinatorics is the branch of combinatorics where the objects of study are subsets of the integers or of other abelian groups, and one is interested in properties and patterns that can be expressed in terms of linear equations. More generally, arithmetic combinatorics deals with properties and patterns that can be expressed via additions and multiplications. In the past ten years, add...
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