Ultraproducts and metastability

2013/01/14 by Jeremy Avigad, Avigad, Jeremy, José Iovino +1
Computer Science · Mathematics · #03C20 #37A30 #46B08 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #Mathematical Dynamics and Fractals #math.DS #math.FA #math.LO #msc:03C20 #msc:37A30 #msc:46B08

paper · pdf · doi:10.48550/arxiv.1301.3063

openalex publication_date 2013/01/14 · arxiv created 2013/10/16 · arxiv updated 2013/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory.

Citations

• On the speed of convergence in the ergodic theorem

Related

• Metastable convergence and logical compactness
• Pseudocompactness and the Uniform Metastability Principle in Model Theory
• Rates of metastability for iterations on the unit interval
• Bounds for a nonlinear ergodic theorem for Banach spaces
• On soft capacities, quasi-stationary distributions and the pathwise approach to metastability