5 papers
Measure Theory in Convergence Spaces Part II: Abstract Integration in Net Convergence Structures
Alexandre Reggiolli Teixeira
The construction of a coherent and general integration procedure is the central question of this second part of our study of measure theory in convergence spaces. We define, and es…
Measure Theory in Convergence Spaces Part I: Sion-Carathéodory Extension in Net Convergence Groups
Alexandre Reggiolli Teixeira
We establish a Carathéodory-type extension theorem for premeasures with values in general separated abelian net convergence groups. Starting from hereditary exhaustivity on the sou…
Sewing on Thin Groupoids, Knitting, and Based Holonomy for Lipschitz Paths
Alexandre Reggiolli Teixeira
An approximate action of the pair groupoid of a metric space determines an action of its Lipschitz-thin groupoid on complete extended metric fibers, uniquely characterized by its l…
Control Measures for Bochner -Valued Vector Measures
Lech Drewnowski, Alexandre Reggiolli Teixeira
It is shown that for any finite positive measure defined on a measure space , and any Banach or Fréchet space , the control measure Theorem of Talagrand (T) is true…
Abstract Integration in Net Convergence Structures
Alexandre Reggiolli Teixeira
In this article, we propose a general theory of integration of the Riemann and Lebesgue types with respect to arbitrary measures and functions, connected by a continuous bilinear p…