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Positivity

, Volume 18, Issue 3, pp 489–503 | Cite as

On the Lebesgue decomposition for non-additive functions

  • Paola CavaliereEmail author
  • Paolo de Lucia
  • Anna De Simone
  • Flavia Ventriglia
Article
  • 165 Downloads

Abstract

A Lebesgue decomposition theorem for non-additive functions, acting on a \(\sigma \)-complete orthomodular lattice and taking values in Hausdorff uniform spaces, is established. No algebraic structure is required on target spaces. The Boolean case is also investigated.

Keywords

Non-additive functions Orthomodular structures  Decomposition theorems 

Mathematics Subject Classification (2000)

Primary 28B99 Secondary 03G12 28A12 06C15 

Notes

Acknowledgments

The authors wish to thank the referee for his/her careful reading of the manuscript and for useful comments.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Paola Cavaliere
    • 1
    Email author
  • Paolo de Lucia
    • 2
  • Anna De Simone
    • 2
  • Flavia Ventriglia
    • 2
  1. 1.Dipartimento di MatematicaUniversità di SalernoFiscianoItaly
  2. 2.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università “Federico II”NaplesItaly

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