Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Finitary imbeddings of certain generalized sample spaces


Authors: Marie A. Gaudard and Robert J. Weaver
Journal: Trans. Amer. Math. Soc. 207 (1975), 293-307
MSC: Primary 81.06
MathSciNet review: 0373474
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A generalized sample space each of whose subspaces has as its logic an orthomodular poset is called an HD sample space. In this paper it is shown that any HD sample space may be imbedded in a natural way in a generalized sample space which is HD and at the same time admits a full set of dispersion free weight functions.


References [Enhancements On Off] (What's this?)

  • [1] Garrett Birkhoff, Lattice theory, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
  • [2] J. C. Dacey, Orthomodular spaces and additive measurement, Caribbean J. Sci. Math. 1 (1969), no. 2, 51–67. MR 0376468
  • [3] D. J. Foulis and C. H. Randall, Operational statistics. I. Basic concepts, J. Mathematical Phys. 13 (1972), 1667–1675. MR 0416417
  • [4] M. A. Gaudard, Maximal refinement ideals and atomicity in certain generalized sample spaces (in preparation).
  • [5] R. J. Greechie, Orthomodular lattices admitting no states, J. Combinatorial Theory Ser. A 10 (1971), 119–132. MR 0274355
  • [6] A. Kolmogoroff, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer-Verlag, Berlin-New York, 1977 (German). Reprint of the 1933 original. MR 0494348
  • [7] G. W. Mackey, The mathematical foundations of quantum mechanics: A lecturenote volume. Benjamin, New York, 1963. MR 27 #5501.
  • [8] C. H. Randall and D. J. Foulis, An approach to empirical logic, Amer. Math. Monthly 77 (1970), 363–374. MR 0258688
  • [9] D. J. Foulis and C. H. Randall, Lexicographic orthogonality, J. Combinatorial Theory Ser. A 11 (1971), 157–162. MR 0280420
  • [10] C. H. Randall and D. J. Foulis, Operational statistics. II. Manuals of operations and their logics, J. Mathematical Phys. 14 (1973), 1472–1480. MR 0416418
  • [11] Robert J. Weaver, Admissible operations on sample spaces over the free orthogonality monoid, Colloq. Math. 25 (1972), 319–324. MR 0326788
  • [12] Robert J. Weaver, Closed sets in the free orthogonality monoid, Amer. J. Math. 96 (1974), 593–601. MR 0364043
  • [13] Robert J. Weaver, Refinement conditions on operations in sample spaces, Canad. J. Math. 27 (1975), no. 5, 991–999. MR 0395620

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 81.06

Retrieve articles in all journals with MSC: 81.06


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0373474-2
Keywords: Empirical logic, generalized sample space, HD sample space, logic, complete orthomodular lattice, operation, orthogonal set, scattered set, finitary sample space, idealized point
Article copyright: © Copyright 1975 American Mathematical Society