Abstract
Of concern are some simple criteria about the convergence of sequences of positive linear operators and functionals in the framework of spaces of bounded functions which are continuous on a given subset of their domain. Among other things some applications concerning the behaviour of the iterates of Bernstein operators defined both on [ 0 , 1 ] [0,1] and on the d d -dimensional simplex and hypercube ( d ≥ 1 ) (d\geq 1) are discussed. A final section treats the behaviour of integrated arithmetic means with respect to a probability Borel measure on a convex compact subset K K of a locally convex space. As a consequence a general weak law of large numbers for sequences of K − K- valued random variables is derived.
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