Preliminaries

  • K. L. Chung
  • R. J. Williams
Part of the Probability and Its Applications book series (PA)

Abstract

For each interval I in IR = (−∞, ∞) let B(I) denote the σ-field of Borel subsets of I. For each tIR+ = [0, ∞), let B t denote B([0, t]) and let B denote \(B(I{R_ + }) = {V_{t \in I{R_ + }}}\)B t — the smallest σ-field containing B t for all t in IR+. Let \(overline {I{R_ + }} = [0,\infty ]\) and \(overline B\) denote the Borel σ-field of \(overline {I{R_ + }}\) generated by B and the singleton {∞}. Let λ denote the Lebesgue measure on IR.

Keywords

Filtration 

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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • K. L. Chung
    • 1
  • R. J. Williams
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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