Invariance principles for sums of Banach space valued random elements and empirical processes

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Summary

Almost sure and probability invariance principles are established for sums of independent not necessarily measurable random elements with values in a not necessarily separable Banach space. It is then shown that empirical processes readily fit into this general framework. Thus we bypass the problems of measurability and topology characteristic for the previous theory of weak convergence of empirical processes.

Both authors were partially supported by NSF grants. This work was done while the second author was visiting the M.I.T. Mathematics Department