Representation of an abstract measure using Borel-isomorphism types

Shortt, R. M.

doi:10.1090/S0002-9939-1989-0947317-5

Representation of an abstract measure using Borel-isomorphism types
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by R. M. Shortt PDF

Proc. Amer. Math. Soc. 105 (1989), 609-614 Request permission

Abstract:

For $X \subseteq R$, the mapping $t$ which assigns to each Borel subset of $X$ its isomorphism type is an abstract measure. Given a monoid-valued measure $m$, we ask when there is an $X \subseteq R$ such that $t$ and $m$ are isomorphic as measures.

References

Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
Rolando Chuaqui, Cardinal algebras and measures invariant under equivalence relations, Trans. Amer. Math. Soc. 142 (1969), 61–79. MR 245743, DOI 10.1090/S0002-9947-1969-0245743-5
K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
R. M. Shortt, Representation of Borel isomorphism by a probability measure, Proc. Amer. Math. Soc. 104 (1988), no. 1, 284–286. MR 958084, DOI 10.1090/S0002-9939-1988-0958084-2

Dissertationes Mathematicae

Alfred Tarski, Cardinal Algebras. With an Appendix: Cardinal Products of Isomorphism Types, by Bjarni Jónsson and Alfred Tarski, Oxford University Press, New York, N. Y., 1949. MR 0029954