Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

, Volume 62, Issue 4, pp 509–552

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

  • R. M. Dudley
  • Walter Philipp

DOI: 10.1007/BF00534202

Cite this article as:
Dudley, R.M. & Philipp, W. Z. Wahrscheinlichkeitstheorie verw Gebiete (1983) 62: 509. doi:10.1007/BF00534202


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.

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • R. M. Dudley
    • 1
  • Walter Philipp
    • 2
  1. 1.M.I.T.CambridgeUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA