Ultraproducts and metastability

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.

References in corpus (2)

• Local stability of ergodic averages
• Metastable convergence theorems

Cited by in corpus (2)

• Categorical semantics of metric spaces and continuous logic
• On the speed of convergence in the ergodic theorem for shift operators