Mathematics Senior Capstone Papers
Document Type
Article
Publication Date
Spring 2024
Abstract
Two specific notions of integration were the motivation of this paper: Riemann-Stieltjes and Lebesgue-Stieltjes integration. The question that arose from these notions was the idea of generalization. How can Stieltjes integration be generalized to an arbitrary measure? The buildup to this question requires a beautiful combination of measure theory and order theory to deliver a measure on totally ordered sets that provide structure for a potential generalization. This paper shows that the set of chains in a totally ordered set is a σ-algebra and defines cumulative cardinality measure on (X, Σ) in an attempt to give insight on the structure of a totally ordered set X as a measurable space.
Recommended Citation
Whitehurst, Gregory, "Abstract Measures on Totally Ordered Sets" (2024). Mathematics Senior Capstone Papers. 46.
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/46