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dc.contributor.advisorFrenzen, Chris
dc.contributor.authorMcInnis, Erik O.
dc.dateSeptember 2002
dc.date.accessioned2012-03-14T17:43:22Z
dc.date.available2012-03-14T17:43:22Z
dc.date.issued2002-09
dc.identifier.urihttp://hdl.handle.net/10945/4857
dc.description.abstractIt is generally accepted that the Riemann integral is more useful as a pedagogical device for introductory analysis than for advanced mathematics. This is simply because there are many meaningful functions that are not Riemann integrable, and the theory of Riemann integration does not contain su.ciently strong convergence 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 signi.cantly more complicated and require a considerable foundation in measure theory. There is now an impetus to accept the gauge integral as a possible new standard in mathematics. This relatively recent integral possesses the intuitive description of the Riemann 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.en_US
dc.description.urihttp://archive.org/details/gaugeintegration109454857
dc.format.extentx, 51 p.en_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.lcshIntegralsen_US
dc.subject.lcshHenstock-Kurzweil integralen_US
dc.subject.lcshRiemann integralen_US
dc.titleGauge integrationen_US
dc.typeThesisen_US
dc.contributor.secondreaderMansager, Bard
dc.contributor.corporateNaval Postgraduate School
dc.contributor.departmentMathematics
dc.subject.authorGauge integrationen_US
dc.subject.authorKurzweilen_US
dc.subject.authorHenstocken_US
dc.subject.authorHK-integralen_US
dc.subject.authorGeneralized Riemannen_US
dc.description.serviceMajor, United States Marine Corpsen_US
etd.thesisdegree.nameM.S. in Applied Mathematicsen_US
etd.thesisdegree.levelMastersen_US
etd.thesisdegree.disciplineApplied Mathematicsen_US
etd.thesisdegree.grantorNaval Postgraduate Schoolen_US
etd.verifiednoen_US
dc.description.distributionstatementApproved for public release; distribution is unlimited.


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