Eugene Bilokopytov - Von Neumann-Maharam problem for vector lattices скачать в хорошем качестве

Eugene Bilokopytov - Von Neumann-Maharam problem for vector lattices

This talk was part of the Workshop on "Structures in Banach Spaces" held at the ESI March 17 - 21, 2025. The classical Von Neumann-Maharam problem asks for a characterization of Boolean algebras which are isomorphic to measure algebras of finite measures. While open ended, this problem has motivated lots of research in Analysis and Set theory. One can take a topological approach to this problem: if a complete Boolean algebra admits a metrizable order continuous uniformly exhaustable locally solid topology, then it is a measure algebra; it is then left to find conditions for existence of such a topology. The goal of the talk is to lay out similar considerations in the context of vector lattices.