A convergence theory approach to definitions of the integral
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Grace Keyser Tennis (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Jerry Vaughan
Abstract: As long ago as 200 B.C., the idea of the integral was known to Archimedes. More than two thousand years later, 1665, Sir Isaac Newton and Gottfried Leibniz simultaneously and independently invented the differential and integral calculus. It was almost another two hundred years before Bernhard Riemann [10] gave the first rigorous definition of the integral. G. Darboux [1] and S. Pollard [9] followed quickly with variations of their own. In 1901, in a very short article for Comptes Rendus [6], Henri Lebesgue gave his definition of the integral. Lebesgue's more general definition of the integral requires the use of measure theory. This is not the case, however, for the integrals recently defined by Edward J. McShane [7], and Ralph Henstock [3], [4]. Their integrals are as general as Lebesgue's but do not require the use of measure theory. The following definition is a polished version of Riemann’s definition.
A convergence theory approach to definitions of the integral
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Created on 1/1/1974
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Additional Information
- Publication
- Thesis
- Language: English
- Date: 1974
- Subjects
- Integral theorems
- Henstock integrals
- Integrals
- Convergence
- Nets (Mathematics)