On the differentiability of arbitrary real-valued set functions. I.
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- by Harvel Wright and W. S. Snyder PDF
- Trans. Amer. Math. Soc. 145 (1969), 439-454 Request permission
References
-
S. Banach, Sur une classe de fonctions d’ensemble, Fund. Math. 6 (1924), 170-188.
- Casper Goffman, Real functions, Rinehart & Co., Inc., New York, N. Y., 1953. MR 0054006
- Hans Hahn and Arthur Rosenthal, Set Functions, University of New Mexico Press, Albuquerque, N.M., 1948. MR 0024504
- W. E. Hartnett and A. H. Kruse, Differentiation of set functions using Vitali coverings, Trans. Amer. Math. Soc. 96 (1960), 185–209. MR 121457, DOI 10.1090/S0002-9947-1960-0121457-9
- Henri Lebesgue, Sur l’intégration des fonctions discontinues, Ann. Sci. École Norm. Sup. (3) 27 (1910), 361–450 (French). MR 1509126, DOI 10.24033/asens.624
- Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957. MR 0082536
- M. E. Munroe, Introduction to measure and integration, Addison-Wesley Publishing Co., Inc., Cambridge, Mass., 1953. MR 0053186
- Anthony P. Morse, A theory of covering and differentiation, Trans. Amer. Math. Soc. 55 (1944), 205–235. MR 9974, DOI 10.1090/S0002-9947-1944-0009974-4 C. Y. Pauc, Review #12195, Math. Reviews 22 (1961), p. 2085. René de Possel, Sur la derivation abstraite des fonctions d’ensembles, C. R. Acad. Sci. Paris 201 (1935), 579. S. Saks, Théorie de l’intégrale, Monografie Matematyczne, vol. II, PWN, Warsaw, 1933; English transl., Monografie Matematyczne, vol. VII, PWN, Warsaw, 1937; 2nd rev. ed., Dover, New York, 1964. A. J. Ward, On the derivation of additive functions of intervals, Fund. Math. 28 (1937), 265-279. R. C. Young, Functions of $\Sigma$ defined by addition or functions of intervals in n-dimensional formulation, Math. Z. 29 (1928), 171-216.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 145 (1969), 439-454
- MSC: Primary 28.16
- DOI: https://doi.org/10.1090/S0002-9947-1969-0251185-9
- MathSciNet review: 0251185