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1966 The theory of stationary point processes
Frederick J. Beutler, Oscar A. Z. Leneman
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Acta Math. 116: 159-190 (1966). DOI: 10.1007/BF02392816


An axiomatic formulation is presented for point processes which may be interpreted as ordered sequences of points randomly located on the real line. Such concepts as forward recurrence times and number of points in intervals are defined and related in set-theoretic Note that for α∈A, Gα may not cover Gα as a convex subgroup and so we cannot use Theorem 1.1 to prove this result. Moreover, all that we know about the Gα/Gα is that each is an extension of a trivially ordered subgroup by a subgroup of R. It B is a plenary subset of A, then there exists a v-isomorphism μ of G into V(B, Gβ/Gβ), but whether or not μ is an o-isomorphism is not known.

Funding Statement

This work was supported by the National Aeronautics and Space Administration under research grant NsG-2-59


Presently at Massachusetts Institute of Technology, Lexington, Mass., U.S.A.


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Frederick J. Beutler. Oscar A. Z. Leneman. "The theory of stationary point processes." Acta Math. 116 159 - 190, 1966.


Received: 29 July 1965; Published: 1966
First available in Project Euclid: 31 January 2017

zbMATH: 0147.16003
MathSciNet: MR199895
Digital Object Identifier: 10.1007/BF02392816

Rights: 1966 © Almqvist & Wiksells Boktryckeri AB


Vol.116 • 1966
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