Large correlated families of positive random variables
1988 ◽
Vol 103
(1)
◽
pp. 147-162
◽
Keyword(s):
S. Argyros and N. Kalamidas([l], repeated in [2], Theorem 6·15) proved the following. If κ is a cardinal of uncountable cofinality, and 〈Eξ〉ξ<κ is a family of measurable sets in a probability space (X, μ) such that infξ<κμEξ = δ, and if n ≥ 1, , then there is a set Γ ⊆ κ such that #(Γ) = κ and μ(∩ξ∈IEξ) ≥ γ whenever I ⊆ ξ has n members. In Proposition 7 below I refine this result by (i) taking any γ < δn (which is best possible) and (ii) extending the result to infinite cardinals of countable cofinality, thereby removing what turns out to be an irrelevant restriction. The proof makes it natural to perform a further extension to general uniformly bounded families of non-negative measurable functions in place of characteristic functions.
1979 ◽
Vol 86
(1)
◽
pp. 103-114
1991 ◽
Vol 14
(2)
◽
pp. 381-384
Keyword(s):
Keyword(s):
1970 ◽
Vol 13
(1)
◽
pp. 151-152
◽