Measurable events indexed by trees

Dodos, P; Kanellopoulos, V; Tyros, K

dc.contributor.author	Dodos, P	en
dc.contributor.author	Kanellopoulos, V	en
dc.contributor.author	Tyros, K	en
dc.date.accessioned	2014-03-01T02:09:30Z
dc.date.available	2014-03-01T02:09:30Z
dc.date.issued	2012	en
dc.identifier.issn	09635483	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29862
dc.subject.other	Cardinalities	en
dc.subject.other	Finite subsets	en
dc.subject.other	Homogeneous tree	en
dc.subject.other	Integer-N	en
dc.subject.other	Probability spaces	en
dc.subject.other	Subtrees	en
dc.subject.other	Computer science	en
dc.subject.other	Probability	en
dc.subject.other	Forestry	en
dc.subject.other	Algorithms	en
dc.subject.other	Forestry	en
dc.subject.other	Probability	en
dc.title	Measurable events indexed by trees	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S0963548312000053	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S0963548312000053	en
heal.publicationDate	2012	en
heal.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 {At:t ∈ T} is a family of measurable events in a probability space (ω,σ,μ) satisfying μ(At)≤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 μ(1∈FAt) ≥θq(b,n) In fact, we can take q(b,n)= ((2b-1)2n-1-1).(2b-2)-1. A finite version of this result is also obtained. © 2012 Cambridge University Press.	en
heal.journalName	Combinatorics Probability and Computing	en
dc.identifier.doi	10.1017/S0963548312000053	en
dc.identifier.volume	21	en
dc.identifier.issue	3	en
dc.identifier.spage	374	en
dc.identifier.epage	411	en