Each Random Variable in separable Banach Space belongs to the Domain of Definition of some inverse to compact linear non-random operator

Abstract

We give in this short report a very simple proof that arbitrary random variable with Borelian distribution in separable Banach space belongs with probability one to a pre-image of some linear compact non-random operator.

References in corpus (5)

• Support of Borelian Measures in Separable Banach Spaces
• CLT for continuous random processes under approximations terms
• Central Limit Theorem and exponential tail estimations in mixed (anisotropic) Lebesgue spaces
• Central limit theorem and exponential tail estimations in hybrid Lebesgue-continuous spaces
• Central Limit Theorem in Holder spaces in the terms of majorizing measures

Cited by in corpus (1)

• Random processes and Central Limit Theorem in Besov spaces