Z. Ergemlidze, A. Shangua, V. Tarieladze
abstract:
Criteria for almost sure boundedness and convergence to zero almost surely of
Banach space valued independent Gaussian random elements are found. The
obtained statements can be viewed as vector-valued versions of the corresponding
results due to N. Vakhania. Moreover, from the obtained statements a strong law
of large numbers is derived in the form of Yu. V. Prokhorov.