Is X(\omega) = \frac{1}{\omega} a Random Variable?

[wayneckm]

Hello all,

I have the following question:

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

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

Thanks.

Wayne

 

[DrRocket]

Hello all,

I have the following question:

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

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

Thanks.

Wayne

No.

Because there is no set of measure 0 on the compliment of which the function is bounded.