Realization of I_p by spaces of random variables

Abstract

Let L ⁰(ΩA,P) be the space of equivalent classes of random variables defined on a probability space (Ω,A,P). Let H be the closed subspace of L ⁰(Ω,A,P) spanned by a sequence of i.i.d. (independent and identically distributed) random variables having the symmetric nondegenerate law F. It is proved that H is linearly homeomorphic to l _p for 0<p≤2 if F belongs to the domain of normal attraction of symmetric stable law withexponent p.

KEY WORDS AND PHRASES:

• Metric linear space
• linear homeomorphism
• symmetric stable laws
• domain of normal attraction
• Khinchine inequality

AMS 1970 subject classification:

• Primary 60B99
• Secondary 46A15