Sequential convergence with exceptional sets

Author

Chaka Karieem Edwards

Date of Award

12-2000

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

G. S. Jordan

Committee Members

Suzanne Lenhart

Abstract

The classical definition of convergence of a sequence {s„} of real numbers may be extended by permitting the defining inequality to fail on an infinite, but relatively small,exceptional set of integers n. In this thesis the cases of exceptional sets of linear density zero and logarithmic density zero are considered. Basic properties of classical convergence are shown to hold for these cases, an example is constructed to show that a set of logarithmic density zero need not have linear density zero, and for each case a Tauberian condition sufficient to deduce classical convergence is provided.

Recommended Citation

Edwards, Chaka Karieem, "Sequential convergence with exceptional sets. " Master's Thesis, University of Tennessee, 2000.
https://trace.tennessee.edu/utk_gradthes/9305