Set-Valued and Variational Analysis

, Volume 26, Issue 4, pp 947–973 | Cite as

Measures and Integrals in Conditional Set Theory

  • Asgar Jamneshan
  • Michael Kupper
  • Martin Streckfuß


The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In particular, this extends the usual representation results for separable spaces.


Conditional set theory Conditional measure theory Vector-valued measure Kernel Conditional distribution 

Mathematics Subject Classification (2010)

03C90 28B15 46G10 60Axx 


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A.J. and M.K. gratefully acknowledge financial support from DFG project KU 2740/2-1. The authors would like to thank an anonymous referee for a careful reading of the manuscript and helpful comments and suggestions.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Asgar Jamneshan
    • 1
  • Michael Kupper
    • 1
  • Martin Streckfuß
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany
  2. 2.Department of MathematicsHumboldt University BerlinBerlinGermany

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