Let {N(t): t≥0} be a nonhomoegneous Poisson process with continuous rate function λ(t)>0. Let T1<T2<... denote the times of the points. Show that

E(|Tn-1||N(1)=n)->1 as n->∞

For nonhomoegneous Poisson process, I know that we have independent increments and that,

Number of points in (t,t+s]

=N(t,t+s] is Poisson distributed with mean

t+s

∫ λ(u)du

t

But do I have to use this? I have no idea where to start and I would appreicate if someone can help.

Thank you!