Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-04T19:10:46.723Z Has data issue: false hasContentIssue false
  • English
  • Français

The existence of locally fine simplicial subdivisions

Part of: Classical measure theory Real functions

Published online by Cambridge University Press:  09 April 2009

W. F. Pfeffer
W. F. Pfeffer
Affiliation:
Department of Mathematics University of CaliforniaDavis, California 95616, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given a simplex S and a positive function δ on S, we show that there is a simplicial subdivision of S such that the diameter of each subdividing simplex is smaller that δ evaluated at some of its vertices.

Keywords

complexpartitionsuperadditive functionlower derivate.

MSC classification

Secondary: 26A39: Denjoy and Perron integrals, other special integrals 28A15: Abstract differentiation theory, differentiation of set functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 114 - 124
Copyright
Copyright © Australian Mathematical Society 1982

References

Dugundji, J. (1966), Topology (Allyn and Bacon, Boston).Google Scholar
Henstock, R. (1968), ‘A Riemann-type integral of Lebesgue power’, Canad. J. Math. 20, 79–87.CrossRefGoogle Scholar
Kuratowski, K. (1966), Topology (Academic Press, New York).Google Scholar
Kurzweil, J. (1957), ‘Generalized ordinary differential equations and continuous dependence on a parameter,’ Czechoslovak Math. J. 82, 418–446.CrossRefGoogle Scholar
Spanier, E. (1966), Algebraic topology (McGraw-Hill, New York).Google Scholar
Whitney, H. (1957), Geometric integration theory (Princeton Univ. Press, Princeton).CrossRefGoogle Scholar