Acta Mathematicae Applicatae Sinica

, Volume 6, Issue 1, pp 81–87 | Cite as

Orthogonal vector measures

  • Jiang Tao 
  • Chen Peide 
Article
  • 15 Downloads

Abstract

This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewitt decomposition theorem for this kind of vector measures. The major results are
  1. (a)

    Any orthogonal vector measure can gain it countable additivity by enlarging its domain;

     
  2. (b)

    Every orthogonal vector measure can be represented as the sum of two orthogonal vector measures, one of which is countably additive, and the other is purely finitely additive. Furthermore, these vector measures are completely perpendicular to each other.

     

Keywords

Major Result Math Application Vector Measure Decomposition Theorem Orthogonal Vector 

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References

  1. [1]
    Chen Peide, Stochastic Measure Theory,Acta Mathematica Sinica,19 (1976), 210–216. (in Chinese)Google Scholar
  2. [2]
    Chen Peide, Orthogonal Stochastic Measures Generated by Squarely Integrable Martinagles,Acta Mathematica Sinica,21 (1978), 363–366. (in Chinese)Google Scholar
  3. [3]
    M. H. Stone, The Theory of Representations for Boolean Algebras,Trans. Amer. Math. Soc.,40 (1936), 37–111.Google Scholar
  4. [4]
    M. H. Stone, Applications of the Theory of Boolean Rings to General Topology,Trans. Amer. Math. Soc.,41 (1937), 375–481.Google Scholar
  5. [5]
    Garret Birkhoff, Lattice Theory, Rev. ed. Amer. Math. Soc. Colloquium Publication, Vol. 25, New York, 1948.Google Scholar
  6. [6]
    K. Yosida, E. Hewitt, Finitely Additive Measures,Trans. Amer. Math. Soc.,72 (1952), 46–66.Google Scholar
  7. [7]
    P. R. Halmos, Measure Theory, Springer-Verlag, New York, 1974.Google Scholar
  8. [8]
    J. Diestel, J. J. Uhl, Jr., Vector Measures, Mathematical Surveys, No. 15, New York, 1977.Google Scholar
  9. [9]
    Chen Peide, General Theory of Stochastic Integral, Lecture Notes of Institute of Applied Mathematics, Academia Sinica, 1977 (in Chinese).Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1990

Authors and Affiliations

  • Jiang Tao 
    • 1
  • Chen Peide 
    • 2
  1. 1.Beijing College of CommerceChina
  2. 2.Institute of Applied MathematicsAcademia SinicaChina

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