## Moving averages.(English)Zbl 0684.60023

Almost everywhere convergence, Proc. Int. Conf., Columbus/OH 1988, 131-144 (1989).
[For the entire collection see Zbl 0679.00012.]
Main aim of the present paper is to discuss possible refinements of the strong law of large numbers for means of i.i.d. random variables $$X;X_ 1,X_ 2,...$$. Several characterizations are obtained in terms of Césaro-, Riesz-, and “moving average”-summability. More general moment conditions than E $$| X|^ p<\infty$$ can be handled by using general self-neglecting functions $$\phi$$ instead of $$\phi (x)=x^{1/p}$$. Finally, it is briefly outlined how the results relate to certain almost sure invariance or non-invariance principles for partial sums. For sake of comparison several references are provided concerning the ergodic, dependent or Banach-valued cases.
Reviewer: J.Steinebach

### MSC:

 60F15 Strong limit theorems 60F17 Functional limit theorems; invariance principles 40G05 Cesàro, Euler, Nörlund and Hausdorff methods

Zbl 0679.00012