Annali di Matematica Pura ed Applicata

, Volume 115, Issue 1, pp 215–223 | Cite as

A characterization theorem for the nearest point mappings of linearC-sets

  • Wayne C. Bell


Suppose U is a set, F is a field of subsets of U, PAB is the set of all bounded finitely additive functions from F into ℝ, and P A + is the set of non-negative valued elements of PAB. In this paper it is proved that if β is a mapping from P A + into P A + then β is the nearest point mapping for a linear C-set iff β commutes with a certain collection of nonlinear mappings.


Nonlinear Mapping Additive Function Point Mapping Characterization Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    W. D. L. Appling,Characterizations of some absolutely continuous additive set functions, Rendiconti del Circolo Matematico di Palermo, serie II, tomo 12 (1963), pp. 347–352.zbMATHMathSciNetGoogle Scholar
  2. [2]
    W. D. L. Appling,Summability of real-valued set functions, Rivista Mathematica, University of Parma,8, no. 2 (1967), pp. 77–100.zbMATHMathSciNetGoogle Scholar
  3. [3]
    W. D. L. Appling,A note on the finite additivity of certain set functions, Bollettino U.M.I.,4, no. 2 (1968), pp. 249–255.MathSciNetGoogle Scholar
  4. [4]
    W. D. L. Appling,Two inclusion theorems for real-valued summable set functions, Rendiconti dei Circolo Matematico di Palermo, series II, tomo 18 (1969).Google Scholar
  5. [5]
    W. D. L. Appling,Integrability and closest approximation representations, Ann. di Mat. Pura et Applic. (to appear).Google Scholar
  6. [6]
    W. D. L. Appling,An isomorphism and isometry theorem for a class of linear functionals, Transactions of the American Mathematical Society,199 (1974), pp. 131–140.CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    W. D. L. Appling,A generalization of absolute continuity and an analogue of the Lebesgue decomposition theorem, Rivista Mathematica, University of Parma, (3)2 (1973), pp. 251–276.zbMATHMathSciNetGoogle Scholar
  8. [8]
    E. Hellinger,Die Orthogonal invarianten Quadratischer Formen von Unendlichvielen Variablen, Dissertation, Gottingen (1907).Google Scholar
  9. [9]
    A. N. Kolmogoroff,Untersuchungen über den Integral begriff, Math. Ann.,103 (1930), pp. 654–696.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • Wayne C. Bell
    • 1
  1. 1.MurrayU.S.A.

Personalised recommendations