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A weak law of large numbers for vector lattice-valued random variables. (English) Zbl 0538.60012
The author introduces the notion of almost uniform convergence for random variables with values in a vector lattice. He proves that the vector lattice of all random variables is closed with respect to this type of convergence. The main result of the paper is a sufficient condition for a sequence of independent, identically distributed random variables to satisfy the weak law of large numbers.

MSC:
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
46A40 Ordered topological linear spaces, vector lattices
46B42 Banach lattices
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