A generalized strong law of large numbers. (English) Zbl 0933.60023

Colubi, Ana; López-Díaz, Miguel; Santos Domínguez-Menchero, J.; Angeles Gil, M.

Probab. Theory Relat. Fields 114, No. 3, 401-417 (1999).

Summary: Strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces. In this paper, a strong law of large numbers which generalizes some previous ones (like those for real-valued random variables and compact random sets) is established. This law is an example of a strong law of large numbers for Borel measurable nonseparably valued elements of a metric space.

MSC:

60F15	Strong limit theorems
03B52	Fuzzy logic; logic of vagueness
60D05	Geometric probability and stochastic geometry

Keywords:

measurable functions; strong law of large numbers; Borel measurable nonseparably valued elements