A new characterization of CesĂ ro-Perron integrals using Peano derivates
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- by J. A. Bergin PDF
- Trans. Amer. Math. Soc. 228 (1977), 287-305 Request permission
Abstract:
The ${Z_n}$-integrals are defined according to the method of Perron using Peano derivates. The properties of the integrals are given including the essential integration by parts theorem. The integrals are then shown to be equivalent to the CesĂ ro-Perron integrals of Burkill.References
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J. C. Burkill, The CesĂ ro-Perron integral, Proc. London Math. Soc. (2) 34 (1932), 314-322.
—. The Cesà ro-Perron scale of integration, Proc. London Math. Soc. (2) 39 (1935), 541-552.
- R. D. James, Generalized $n$th primitives, Trans. Amer. Math. Soc. 76 (1954), 149–176. MR 60002, DOI 10.1090/S0002-9947-1954-0060002-0
- H. William Oliver, The exact Peano derivative, Trans. Amer. Math. Soc. 76 (1954), 444–456. MR 62207, DOI 10.1090/S0002-9947-1954-0062207-1
- I. P. Natanson, Theory of functions of a real variable. Vol. II, Frederick Ungar Publishing Co., New York, 1961. Translated from the Russian by Leo F. Boron. MR 0148805
- Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578
- W. L. C. Sargent, A descriptive definition of Cesà ro-Perron integrals, Proc. London Math. Soc. (2) 47 (1941), 212–247. MR 5897, DOI 10.1112/plms/s2-47.1.212
- S. Verblunsky, On a descriptive definition of Cesà ro-Perron integrals, J. London Math. Soc. (2) 3 (1971), 326–333. MR 286954, DOI 10.1112/jlms/s2-3.2.326
- S. Verblunsky, On the Peano derivatives, Proc. London Math. Soc. (3) 22 (1971), 313–324. MR 285678, DOI 10.1112/plms/s3-22.2.313
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 228 (1977), 287-305
- MSC: Primary 26A39
- DOI: https://doi.org/10.1090/S0002-9947-1977-0435312-0
- MathSciNet review: 0435312