ON INTERSECTION OF PROBLEMS OF THEORETICAL STATISTICS AND SET THEORY

Gogi Pantsulaia (Georgia)

Received December 20, 2007

Abstract

Specialized in Radon metric space, we prove that in the system of axioms (ZFC) and (MA) an arbitrary orthogonal family of probability Borel measures  with  is strictly separated. For an ordinal number  we construct a weakly separated family of probability measures  on the unit square  such that a condition  is equivalent to the condition that a family  is strictly separated.

Keywords and phrases: Martin’s axiom, continuum hypothesis, radon space, separated family of probability measures.