On uniqueness of distribution of a random variable whose independent copies span a subspace in Lp
Abstract
Let 1≤ p<2 and let Lp=Lp[0,1] be the classical Lp-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from Lp spans in Lp a subspace isomorphic to some Orlicz sequence space lM. We present precise connections between M and f and establish conditions under which the distribution of a random variable f whose independent copies span lM in Lp is essentially unique.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.