Hello people, I'm needing some help here.
Is it correct to say that a family of probability measure with finite p-moment is tight?
I saw this result only for gaussians (for p = 2, Billingsley, Probability and Measure, 3ed, page 337).
For example, let Xn be a r.v with finite p-moment. So, by Chebychev inequality,
Pn({x : |x| > c) \leq E|Xn|^p / c^p < K/c^p.
Therefore, taking sup_n in both sides, for a large c,
Pn({x : |x| > c) < \epsilon
and so the family {Pn} is tight. Is it correct?
Thanks in advance.