Effective convergence notions for measures on the real line

Abstract: In classical measure theory, there are two primary convergence notions studied for sequences of measures: weak and vague convergence. In this talk, we discuss a framework to study the effective theory of weak and vague convergence of measures on the real line. For effective weak convergence, we give an effective version of a characterization theorem for weak convergence called the Portmanteau Theorem. We also discuss the relationship between effective weak convergence and the structure of the space of finite Borel measures on the real line as a computable metric space. In contrast to effective weak convergence, we give an example of an effectively vaguely convergent sequence of measures that has an incomputable limit. Nevertheless, we discuss the conditions for which the limit of an effectively vaguely convergent sequence is computable and the conditions for which effective weak and vague convergence of measures coincide. This talk will feature joint work with Timothy McNicholl.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.