Abstract
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
Note
Presently at Massachusetts Institute of Technology, Lexington, Mass., U.S.A.
Citation
Frederick J. Beutler. Oscar A. Z. Leneman. "The theory of stationary point processes." Acta Math. 116 159 - 190, 1966. https://doi.org/10.1007/BF02392816
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