Displaying similar documents to “Characterisation of types of order satisfying α 0 + α 1 = α 1 + α 0 ”

Generalized interval exchanges and the 2–3 conjecture

Shmuel Friedland, Benjamin Weiss (2005)

Open Mathematics

Similarity:

We introduce the notion of a generalized interval exchange φ 𝒜 induced by a measurable k-partition 𝒜 = A 1 , . . . , A k of [0,1). φ 𝒜 can be viewed as the corresponding restriction of a nondecreasing function f 𝒜 on ℝ with f 𝒜 ( 0 ) = 0 , f 𝒜 ( k ) = 1 . A is called λ-dense if λ(A i∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that f 𝒜 ∘ f ℬ = f ℬ ∘ f 𝒜 . We give necessary and sufficient conditions for this equality to hold. We...