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University of Illinois at Urbana-Champaign

The Pettis Integral

Abstract

dc:description

The 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 × 1

Rights

Language dc:language
eng

Identifiers

dc:identifier.*
Identifier
(UMI)AAI8026497
OAI identifier oai:identifier
oai:www.ideals.illinois.edu:2142/68171

Chain of custody

source
Harvested from
University of Illinois - Urbana-Champaign
Base URL
www.ideals.illinois.edu/oai-pmh
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Geitz, Robert Frederick. The Pettis Integral. Dissertation thesis, University of Illinois at Urbana-Champaign, 2014. http://hdl.handle.net/2142/68171