For brevity, we will call all such worlds so related to i, "i-Acceptable" worlds and denote them by Ai.[23] We then add that the acceptability relation is "serial": for every world, i, there is at least one i-acceptable world.
We say that {X i : i ≥ 1} are acceptable if there exists δ > 0, such that for any real λ satisfying | λ | ≤ δ, E exp λ ∑ i = 1 n X i ≤ ∏ i = 1 n E exp { λ X i }, for all n ≥ 1. (1.1).
Write g ( n ) = ∏ i = 1 n 2 ( 1 + c θ i ), obviously the above random variables {X i : i ≥ 1} are widely acceptable, but are not acceptable when θ i > 0, which is resulted from that taking different values for θ i, i ≥ 1 can lead to the corresponding different values for g(n).
Especially, if in (4.2), g(n) ≡ M (≥ 1), the r.v.s {X i : i ≥ 1} are extended acceptable (EA).
She added: "It's a terrible mistake to go through your career, or indeed your life, worrying, 'Do I fit into a groove, am I acceptable?' You've only got what you are and the background you come from and as an actor you try and reinvent yourself according to what parts come in".
Say that the random variables {X i : i ≥ 1} are widely acceptable WA) for δ0 > 0, if for any real 0 < λ ≤ δ0, there exist positive numbers g(n), n ≥ 1, such that E exp λ ∑ i = 1 n X i ≤ g ( n ) ∏ i = 1 n E exp { λ X i } for all n ≥ 1. (4.2).
I'm acceptable and totally accepted".
Is "bloody pom" acceptable?
Is violence ever acceptable?
Is hacking ever acceptable?
Is that still acceptable?
