Hello everyone! I need to solve the following problem but I can't do it.

Let P1 and P2 be two sigma-additive over the set N of natural numbers probabilities such that P1([0,n])>=P2([0,2]) for all n. I know that for sure there exist n1 and n2 such that forall c>0, forall n>=n2 EP2[(x+c)1[0,n]]>EP2[x] and forall n>=n1 EP1[(x+c)1[0,n]]>EP1[x]. With x a non-negative, real-valued, bounded sequence.

I want to prove that P1([0,n])>=P2([0,2]) implies that whenever for an n EP2[(x+c)1[0,n]]>EP2[x] then for the same n EP1[(x+c)1[0,n]]>EP1[x].

Thanks a lot!