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I have the following question:

Assume [tex](\Omega, \mathcal{F},P) = ([0,1],\mathcal{B}([0,1]),\lambda)[/tex], where [tex]\lambda[/tex] is Lebesgue mesure, so is [tex]X(\omega) = \frac{1}{\omega}[/tex] a random variable defined on this probability space?

If yes, then can I say that [tex]X[/tex] is bounded a.s. because the set for unboundedness is [tex]{0}[/tex] which is of measure 0?

Thanks.

Wayne

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# Random Variable

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