probability theory – Is the family $mathcal{U} = leftlbrace Uleft(left[0, nright]right): n in mathbb{N}rightrbrace$ conditionally compact?


Is the family $mathcal{U} = leftlbrace Uleft(left(0, nright)right): n in mathbb{N}rightrbrace$ conditionally compact?

I got hint, that I should use Prokhorov’s theorem (probability calculus), but I don’t know how to proceed from this at all…

All help will be appreciated.