In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relation
Let {(Xi, Si, μi) : i ∈N} be a sequence of probability measure spaces and (↑*Xi, L(↑*Si), L(↑*μi)) be the Loeb measure space with respect to (Xi, Si, μi)