Abstracts: topology, analysis, measure theory

Authors: Bohuslav Balcar, Wieslaw Glowczynski and Thomas Jech
Title: The sequential topology on complete Boolean algebras
Fundamenta Mathematicae 155 (1998)
Abstract: We investigate the sequential topology on a complete Boolean algebra B determined by algebraically convergent sequences in B. We show the role of weak distributivity of B in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for B to carry a strictly positive Maharam submeasure is that B is ccc and that the sequential topology is Hausdorff. We also characterize sequential cardinals.

Author: Thomas Jech
Title: The logarithmic distribution of leading digits and finitely additive measures
Discrete Math. 108 (1992)
Abstract: We state a necessary and sufficient condition for a probability measure to satisfy the first digit law.

Author: Thomas Jech
Title: Local topology and a spectral theorem
Operator Theory 48 (1990)
Abstract: We introduce a generalization of topological spaces, which makes it possible to define, among others, convergence a.e., and to prove an abstract version of the spectral theorem. Our approach is related to Boolean-valued analysis.