The initial integral
DOI:
https://doi.org/10.5902/2179460X24872Abstract
The pourpouse of this work is to define what is understood by initial integral and also to demonstrate that Riemann’s integral over the set R ([a, b]; IR) of the integrable defined in the compact interval [a, b], is an initial integral.
The Arzelà's Dominated Convergence Theorem in Riemann's theory context is demonstrated.
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References
ARZELÀ, C. Sulli Integrazione per Serie, Atti Acc. Lincei Rend, Rome, (4) 1(1885), 532-537.
BISOGNIN, E. A Integral de Riemann Abstrata e o Teorema de Representação de Riesz. Rio de Janeiro. 1979. (Tese de Mestrado- UFRJ).
BOURBAKI, N. Integration, Chap. I, II, III, IV. Paris. 1952.
LUXEMBURG, W.A.J. Arzelà's Dominated Convergence Theorem for the Riemann Integral. American Mathematical Monthly, 78(1971),970-979.
RUDIN, W. Principles of Mathematical Analysis. Third Edition.Mc. Graw-Hill.
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