Problem in the paper of van Zwet

[victoriaabc]

Hi all,

Please help! I am reading the paper "A note on contiguity and Hellinger distance" by J. Oosterhoff and W.R. van Zwet. I have tons of questions. The following is just one of them.

Question 1: in their paper, when they prove the asymptotic normality they claim that according to an equivalent form of the normal convergence theorem (from Loeve's book) they can obtain that conditions (3.2) and (3.3) are equivalent to (3.8)-(3.10). Is there anyone know how they got there?

I am sorry that I am unable to type the formula down, there are too many notations. If anyone is familiar with this paper, could you please kindly help me out? Thank you very much.

 

[WWGD]

Why don't you scan the pages and post them as a .gif or .jpeg

 

[victoriaabc]

Why don't you scan the pages and post them as a .gif or .jpeg

Hi WWGD,

Thank you for your suggestion. Attached are the pages. I highlighted the part that I have problems. Besides my previous question, I am also wondering if there is any example satisfying those conditions (3.4)-(3.6) in their normality theorem? Anyone can give me a hint?

Thank you very much for all your help.