Mesures invariantes par translation, classes de Dynkin first-digit problem. (Translation invariant measures; first-digit problem Dynkin classes)
type: Item
instance of: scholarly article
title: Mesures invariantes par translation, classes de Dynkin first-digit problem. (Translation invariant measures; first-digit problem Dynkin classes)
zbMATH Open document ID: 0627.28010
DOI: 10.1016/0001-8708(85)90004-0
author: Jianyong Qiao
author: Sumit K. Garg
published in: Advances in Mathematics
publication date: 1985-01-01T00:00:00Z
review text: In the first 4 sections of this long and interesting paper the authors study asymptotic and analytic densities of some subsets of \({\mathbb{N}}^*\) by means of the notion of finitely additive measures on algebras. They also give a solution to the first-digit problem [cf., e.g. \textit{B. J. Flehinger}, Am. Math. Mon. 73, 1056-1061 (1966; Zbl 0147.175)]. In Sections 6 and 7, they present a general theory of \(\alpha\)-classes (algebras of subsets of \({\mathbb{N}}^*\) which are stable under translation and ``homothety'') and measures over these \(\alpha\)-classes. In the last two sections, a link is established between the notion of natural integrability and the notion of a net of probability measures over \({\mathcal P}({\mathbb{N}}^*)\), which are \(\sigma\)-additive and asymptotically invariant under translation. Finally, a generalization is obtained of the criterion of natural integrability of \textit{L. E. Dubins} and \textit{D. Margolies} [Naturally integrable functions, Univ. of California, Berkeley, per. bibl.].
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 11K16
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 4019385
zbMATH Keywords: translation invariant measures
zbMATH Keywords: Dynkin class
zbMATH Keywords: finitely additive measures
zbMATH Keywords: first-digit problem
zbMATH Keywords: algebras of subsets
zbMATH Keywords: natural integrability
zbMATH Keywords: net of probability measures
MaRDI profile type: Publication
full work available at URL: 0001-8708(85)90004-0
OpenAlex ID: W1972582567
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description: scientific article; zbMATH DE number 4019385