Realization ofIpby spaces of random variables

摘要

LetL0(#x3A9;A,P) be the space of equivalent classes of random variables defined on a probability space (#x3A9;,A,P). LetHbe the closed subspace ofL0(#x3A9;,A,P) spanned by a sequence of i.i.d. (independent and identically distributed) random variables having the symmetric nondegenerate lawF. It is proved thatHis linearly homeomorphic tolpfor 0p#x2264;2 ifFbelongs to the domain of normal attraction of symmetric stable law withexponentp.