Abstract
dc:descriptionThe Pettis integral of a weakly measurable vector-valued function is the most natural integral for use in Banach spaces. Although first defined over forty years ago, the integral has stubbornly defied analysis and has long been considered unmanageable. My thesis presents the first successful analysis of the Pettis integral. I show that a slight restriction on the measure spaces under consideration leads to a theory of Pettis integration very analogous to the theory of the better known, but more restrictive, Bochner integral. The resulting characterization of the Pettis integrable functions is much simpler than was previously believed possible.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Geitz, Robert Frederick
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8026497
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/68171