Marcinkiewicz-Zygmund Weak Laws of Large Numbers for Unconditional Random Elements in Banach Spaces

摘要

Convergence in probability is obtained for random elements in Banach spaces satisfying various distributional conditions including independence, conditional independence, and unconditional semi-basic, and weights. The constant p, 1 < or = p < or = 2, is related to a geometric property of the Banach space and to moment conditions. These results relax the usual hypothesis of identical distributions to tightness and are for conditionally independent and unconditionally semi-basic random elements which are more general than independent random elements with zero means.