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Convergence of non increasing sequence of random number

  1. Dec 31, 2012 #1
    I have a non-increasing sequence of random variables [itex] \{Y_n\}[/itex] which is bounded below by a constant [itex]c[/itex], [itex]\forall \omega \in \Omega[/itex]. i.e [itex]\forall \omega \in \Omega[/itex], [itex]Y_n \geq c[/itex], [itex]\forall n[/itex]. Is it true that the sequence will converge to [itex]c[/itex] almost surely?

  2. jcsd
  3. Dec 31, 2012 #2


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    Hint: If c is such a constant, what about c-1?
  4. Dec 31, 2012 #3
    All the elements of the sequence are bounded below by c. So, I am not sure what are you trying to say. can you please elaborate?
  5. Jan 1, 2013 #4


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    His point is that if the set is bounded below by c, it is also bounded below by c-1 or, for that matter any number less than c. Just saying "bounded below by c" does NOT tell you very much. You seem to be confusing "lower bound" with "greatest lower bound".
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