Show that if http://www.sosmath.com/CBB/latexrend...208c27ef3b.gif are independent random variables.then

If http://www.sosmath.com/CBB/latexrend...76d8574b61.gif almost surely then http://www.sosmath.com/CBB/latexrend...6f9d7ed16d.gif for some A.

It looks like Kolmogorov's onezero law. We know limsup of an independent random variables belongs to the tail algebra, can we claim the same for the sup ? Also, how do we find such number A?

Regards, hermanni.