Download PDF - Algebraic ramifications of the common extension problem for group-valued measuresAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Algebraic ramifications of the common extension problem for group-valued measures

Authors 1, 2

Affiliations

  1. Fachbereich 6-Mathematik, Universität GHS, 45117 Essen, Germany
  2. Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459-0128, U.S.A.

Abstract

Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.

Bibliography

  1. A. Basile and K. P. S. Bhaskara Rao, Common extensions of group-valued charges, Boll. Un. Mat. Ital. 7 (5-A) (1991), 157-162.
  2. A. Basile, K. P. S. Bhaskara Rao and R. M. Shortt, Bounded common extensions of bounded charges, Proc. Amer. Math. Soc. 121 (1994), 137-143.
  3. K. P. S. Bhaskara Rao and R. M. Shortt, Common extensions for homomorphisms and group-valued charges, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 125-140.
  4. K. P. S. Bhaskara Rao and R. M. Shortt, Group-valued charges: common extensions and the finite Chinese remainder property, Proc. Amer. Math. Soc. 113 (1991), 965-972.
  5. T. Carlson and K. Prikry, Ranges of signed measures, Period. Math. Hungar. 13 (1982), 151-155.
  6. S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235.
  7. L. Fuchs, Infinite Abelian Groups, Vols. I and II, Academic Press, New York, 1970 & 1973.
  8. R. Göbel and R. Prelle, Solution of two problems on cotorsion abelian groups, Arch. Math. (Basel) 31 (1978), 423-431.
  9. Z. Lipecki, On common extensions of two quasi-measures, Czechoslovak Math. J. 36 (1986), 489-494.
  10. E. Marczewski, Measures in almost independent fields, Fund. Math. 38 (1951), 217-229.
  11. K. M. Rangaswamy and J. D. Reid, Common extensions of finitely additive measures and a characterization of cotorsion Abelian groups, in: Proc. Curacao, Abelian Groups, Marcel Dekker, New York, 1993, 231-238.
  12. L. Salce, Cotorsion theories for abelian groups, Symposia Math. 23 (1979), 11-32.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm146/fm14611.pdf

Fundamenta Mathematicae
1994-1995/146/1
Export to PBN, Opens in new tab
Pages:
1-20
Main language of publication
English
Received
1993-03-10
Accepted
1993-11-16
Published
1994
Exact and natural sciences