On the Limit Behavior of a Class of Empirical Means of a Random Set

Abstract

Previous article Next article On the Limit Behavior of a Class of Empirical Means of a Random SetS. A. KovyazinS. A. Kovyazinhttps://doi.org/10.1137/1130101PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. Matheron, Random sets and integral geometry, John Wiley & Sons, New York-London-Sydney, 1975xxiii+261 52:6828 0321.60009 Google Scholar[2] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 34:3596 0108.14202 Google Scholar[3] O. Yu. Vorob'ev, On the multivariate characteristics of states of distributed probability processes, Izv. SO Akad. Nauk SSSR, 3 (1977), 3–7, Ser. Tekhn. Nauk, 1, pp. 3–7. (In Russian.) Google Scholar[4] O. Yu. Vorob'ev and , E. N. Valendik, Probabilistic Multivariate Modelling, Nauka, Novosibirsk, 1978, (In Russian.) Google Scholar[5] V. V. Bazhenov, Problems of control of localization control by planar propagation processes, Izv. Akad. Nauk SSSR, 3 (1979), 64–72, (In Russian.) Google Scholar[6] S. A. Kovyazin, On a description of random sets in terms of measure theory, Part 2, 1982, Preprint VTs SO Akad. Nauk SSSR, Krasnoyarsk, no. 11. (In Russian.) Google Scholar[7] S. A. Kovyazin, A variant of the law of large numbers for random subsets of a space with an atomless measure, 1983, Preprint VTs SO Akad. Nauk SSSR, Krasnoyarsk, no. 1, pp. 8–9. (In Russian.) Google Scholar[8] A. I. Orlov, Random sets: laws of large numbers and the testing of statistical hypotheses, Theory Prob. Appl., 23 (1978), Google Scholar[9] Zvi Artstein and , Richard A. Vitale, A strong law of large numbers for random compact sets, Ann. Probability, 3 (1975), 879–882 52:6825 0313.60012 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Random Closed Sets and Capacity Functionals10 November 2017 Cross Ref Expectations of Random Sets10 November 2017 Cross Ref Minkowski Sums10 November 2017 Cross Ref Unions of Random Sets10 November 2017 Cross Ref Random Sets and Random Functions10 November 2017 Cross Ref References7 April 2015 Cross Ref Level sets estimation and Vorob’ev expectation of random compact setsSpatial Statistics, Vol. 2 Cross Ref Volume 30, Issue 4| 1986Theory of Probability & Its Applications History Submitted:07 June 1984Published online:28 July 2006 InformationCopyright © 1986 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130101Article page range:pp. 814-820ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics