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- W2123194426 abstract "A tree T is said to be homogeneous if it is uniquely rooted and there exists an integer b ≥ 2, called the branching number of T , such that every t ∈ T has exactly b immediate successors. We study the behaviour of measurable events in probability spaces indexed by homogeneous trees. Precisely, we show that for every integer b ≥ 2 and every integer n ≥ 1 there exists an integer q ( b , n ) with the following property. If T is a homogeneous tree with branching number b and { A t : t ∈ T } is a family of measurable events in a probability space (Ω,Σ,μ) satisfying μ( A t )≥ϵ>0 for every t ∈ T , then for every 0<θ<ϵ there exists a strong subtree S of T of infinite height, such that for every finite subset F of S of cardinality n ≥ 1 we have In fact, we can take q ( b , n )= ((2 b −1) 2 n −1 −1)·(2 b −2) −1 . A finite version of this result is also obtained." @default.
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- W2123194426 date "2012-03-12" @default.
- W2123194426 modified "2023-09-23" @default.
- W2123194426 title "Measurable Events Indexed by Trees" @default.
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- W2123194426 doi "https://doi.org/10.1017/s0963548312000053" @default.
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