Convergence of Sequences I

  • Phoebus J. Dhrymes


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
$$ \sum\limits_{{i = 1}}^{\infty } {{{{\left( { - 1} \right)}}^{i}}} $$


Probability Space Independent Random Variable Measure Zero Uniform Integrability Tail Event 
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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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