Abstract: Specialized in Radon metric space, we prove that in the
system ofaxioms (ZFC)
and (MA) an arbitrary orthogonal
family of probability Borel measures with is strictly separated. Foran ordinal number we construct a weakly separatedfamily of probabilitymeasuresontheunit 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.
