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Convergence of Sequences I

  • Phoebus J. Dhrymes

Abstract

In this chapter, we shall examine issues that relate to the manner in which sequences of random variables approach a limit. When we deal with sequences or series of real numbers, such issues are rather simple in their resolution, i.e., the sequence either has a unique limit or it may have several limit points; and a series may either converge to a finite number or diverge (to ±∞) or it may have no limit point, as, for example, the series
$$ \sum\limits_{{i = 1}}^{\infty } {{{{\left( { - 1} \right)}}^{i}}} $$
.

Keywords

Probability Space Independent Random Variable Measure Zero Uniform Integrability Tail Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1989

Authors and Affiliations

  • Phoebus J. Dhrymes
    • 1
  1. 1.Department of EconomicsColumbia UniversityNew YorkUSA

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