Name
Abstract | ||
|---|---|---|
A tree T is said to be homogeneous if it is uniquely rooted and there exists an integer b â聣楼 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 â聣楼 2 and every integer n â聣楼 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)â聣楼脧µ0 for every t ∈ T, then for every 0S of T of infinite height, such that for every finite subset F of S of cardinality n â聣楼 1 we have \[ \mu\biggl( \bigcap_{t\in F} A_t\biggr) \meg \theta^{q(b,n)}. \] In fact, we can take q(b,n)= ((2b-1)2n-1-1)ï戮·(2b-2)-1. A finite version of this result is also obtained. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1017/S0963548312000053 | Combinatorics, Probability & Computing |
Keywords | Field | DocType |
finite subset f,probability space,following property,number b,integer n,measurable event,cardinality n,integer q,finite version,homogeneous tree,satisfiability,indexation | Integer,Discrete mathematics,Combinatorics,Probability space,Homogeneous,Measure (mathematics),Homogeneous tree,Mathematics,Branching (version control) | Journal |
Volume | Issue | ISSN |
21 | 3 | Combinatorics, Probability and Computing 21 (2012), 374-411 |
Citations | PageRank | References |
2 | 0.43 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pandelis Dodos | 1 | 5 | 2.33 |
| V. Kanellopoulos | 2 | 7 | 2.66 |
| Konstantinos Tyros | 3 | 6 | 2.63 |