Solovay model and duality principle between the measure and the Baire category in a Polish topological vector space $H(X,S,\mu)$

TL;DR

This paper demonstrates that in the Solovay model, a duality principle linking measure and Baire category holds for the domain of generalized integrals in a Polish topological vector space, highlighting foundational measure-category relationships.

Contribution

It establishes a duality principle between measure and Baire category within the Solovay model for vector-function integrals in Polish spaces, a novel theoretical insight.

Findings

Duality principle holds in Solovay model

Domain of generalized integral is of first category

Connects measure theory and Baire category in vector spaces

Abstract

In Solovay model it is shown that the duality principle between the measure and the Baire category holds true with respect to the sentence - "The domain of an arbitrary generalized integral for a vector-function is of first category."