an:03940292
Zbl 0586.60007
Mikosch, T.; Norvaisa, R.
Strong laws of large numbers for fields of Banach space valued random variables
EN
Probab. Theory Relat. Fields 74, 241-253 (1987).
00151603
1987
j
60B12 60G60 60F15
fields of Banach space valued random variables; strong law of large numbers; weighted sums; Marcinkiewicz-Zygmund laws
The aim of this paper is to give necessary and sufficient conditions for the applicability of the strong law of large numbers (SLLN) to rectangular sums of independent random variables taking values in a real separable Banach space B. The basic tool is a Prokhorov-type criterion about the SLLN which is independent on the geometry of B, but is strongly dependent on the form of the norming constants. This criterion is applied in order to prove a general SLLN for weighted sums and Marcinkiewicz- Zygmund laws.
The connection between the geometry of B and the SLLN for several norming constants is also investigated.