Pseudo-uniform convergence,

a nonstandard treatment

Author:
Nader Vakil

Journal:
Proc. Amer. Math. Soc. **126** (1998), 809-814

MSC (1991):
Primary 46S20, 03H05

DOI:
https://doi.org/10.1090/S0002-9939-98-04312-3

MathSciNet review:
1443413

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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce and study the notion of pseudo-uniform convergence which is a weaker variant of quasi-uniform convergence. Applications include the following nonstandard characterization of weak convergence. Let be an infinite set, the Banach space of all bounded real-valued functions on a bounded sequence in and Then the sequence converges weakly to if and only if the convergence is pointwise on and, for each strictly increasing function , each , and each , there is an unlimited such that .

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Additional Information

**Nader Vakil**

Affiliation:
Department of Mathematics, Western Illinois University, Macomb, Illinois 61455

Email:
N-Vakil@bgu.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04312-3

Received by editor(s):
October 31, 1995

Received by editor(s) in revised form:
September 6, 1996

Communicated by:
Andreas R. Blass

Article copyright:
© Copyright 1998
American Mathematical Society