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The research presented in this paper was motivated by our aim to study a problem due to J. Bourgain [3]. The problem in question concerns the uniform bound-edness of the classical separation rank of the elements of a separable compact set of the first Baire class. In the sequel we shall refer to these sets (separable or non-separable) as Rosenthal compacta… (More)

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 behavior 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… (More)

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. A vector homogeneous tree T is a finite sequence (T 1 , ..., T d) of homogeneous trees and its level product ⊗T is the subset of the cartesian product T 1 × ... × T d… (More)

We show that for every rooted, finitely branching, pruned tree T of height ω there exists a family F which consists of order isomorphic to T subtrees of the dyadic tree C = {0, 1} <N with the following properties: (i) the family F is a G δ subset of 2 C ; (ii) every perfect subtree of C contains a member of F ; (iii) if K is an analytic subset of F , then… (More)

We introduce the notion of an M-family of infinite subsets of N which is implicitly contained in the work of A. R. D. Mathias. We study the structure of a pair of orthogonal hereditary families A and B, where A is analytic and B is C-measurable and an M-family.

We prove a variant of the abstract probabilistic version of Szemerédi's regularity lemma, due to Tao, which applies to a number of structures (including graphs, hy-pergraphs, hypercubes, graphons, and many more) and works for random variables in L p for any p > 1. Our approach is based on martingale difference sequences.

For every integer k 2 let [k] <N be the set of all words over k. A Carlson–Simpson tree of [k] <N of dimension m 1 is a subset of [k] <N of the form {w} ∪ w w 0 (a 0) ... where w is a word over k and (wn) m−1 n=0 is a finite sequence of left variable words over k. We study the behavior of a family of measurable events in a probability space indexed by the… (More)

- Apostolos Krallis, Prokopis Pladis, Vassilis Kanellopoulos, Vassilis Saliakas, Vassilis Touloupides, Costas Kiparissides
- 2010

As the polymer industry becomes more global and competitive pressures are intensifying, polymer manufacturers recognize the need for the development of advanced process simulators for polymer plants. The overall goal is to utilize powerful, flexible, adaptive design and predictive simulation tools that can follow and predict the behaviour of polymer… (More)

- V Kanellopoulos, And K Tyros
- 2009

We give an alternative proof of W.T. Gowers' theorem on block bases in Banach spaces by reducing it to a discrete analogue on specific count-able nets.