Liftings for abstract valued functions and separable stochastic processes

  • A. Ionescu Tulcea
  • C. Ionescu Tulcea


In this paper we extend the notion of lifting from real-valued functions to abstract-valued functions (functions with values in a completely regular space). We prove the existence and uniqueness of the “abstract lifting” associated with a given “real lifting”. As an application we show that given a stochastic process with values in a completely regular space, the modification of this process obtained by applying a lifting is always separable.


Stochastic Process Probability Theory Mathematical Biology Regular Space Abstract Lift 
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Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • A. Ionescu Tulcea
    • 1
  • C. Ionescu Tulcea
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

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