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Convergence of non increasing sequence of random number 
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#1
Dec3112, 01:58 AM

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I have a nonincreasing 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?
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#2
Dec3112, 10:49 AM

Mentor
P: 11,602

Hint: If c is such a constant, what about c1?



#3
Dec3112, 06:45 PM

P: 2




#4
Jan113, 04:24 AM

Math
Emeritus
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Thanks
PF Gold
P: 39,345

Convergence of non increasing sequence of random number
His point is that if the set is bounded below by c, it is also bounded below by c1 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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