Gauge Integration
Abstract
It is generally accepted that the Riemann integral is more useful as a pedagogical device for introductory analysis than for advanced mathematics. This is simple because there are many meaningful functions that are not Riemann integrable and the theory of Riemann integration does not contain sufficiently strong convenience theorems. Lebesgue developed his theory of measure and integration to address these shortcomings. His integral is more powerful in the sense that it integrates more functions and possesses more general convergence theorems. However, his techniques are significantly more complicated and require a considerable foundation in measure theory. There is not an impetus to accept the gauge integral as a possible new standard in mathematics. This relatively recent integral possesses the intuitive description of the Rienmann integral, with the power of the Lebesgue integral. The purpose of this thesis is to explore the basis of gauge integration theory through its associated preliminary convergence theorems, and to contrast it with other integration techniques through explicit examples.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 2002
- Accession Number
- ADA407084
Entities
People
- Erik O. Mcinnis
Organizations
- Naval Postgraduate School