According to Theorem 1.3, the analytic study of (p ij ) is reduced to that of (П IJ if the set of indices F is ignored. In fact, the curtailed matrix (p ij ), i, jIF, is a transition matrix and its elements differ from those of П IJ only in certain constant factors depending on the second index. From the standpoint of probability, it will be seen (in § 4) that the set F plays a nuisance role and can indeed be ignored. Moreover, the reduction from (P ij ) to (П IJ is also justified on probabilistic grounds (see Theorem 4.3). The distinctive feature of the transition matrix (П IJ ) is the property (1.14) which will now be formulated as a definition.


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Copyright information

© Springer-Verlag OHG. Berlin · Göttingen · Heidelberg 1960

Authors and Affiliations

  • Kai Lai Chung
    • 1
  1. 1.Syracuse UniversityUSA

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