Geodesic
Additivity of the Pn -Integral (2)
Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 506-512

Voir la notice de l'article provenant de la source Cambridge University Press

The problem of additivity of the Pn -integral on abutting intervals was considered in [2] and in [5]. It was noted in [2] that the necessary and sufficient conditions for additivity for the P 2-integral obtained by Skvorcov in [5] could be completely generalized to the Pn -integral, n> 2, if a key lemma (corresponding to Skvorcov's Lemma 3 [6]) could be proved. We provide a proof of that lemma in this paper and hence obtain the general additivity result.The definitions and notation of [2] are used in the following, except that we shall take the following as the definition of Pn -major and minor functions: Definition 1.1. Let f(x) be a function defined in [a, b] and let a 1, i = 1, 2, ..., n, be fixed points such that a = a 1 < a 2 < ... < an = b. 
Cross, G. E. Additivity of the Pn -Integral (2). Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 506-512. doi: 10.4153/CJM-1982-034-3
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