Mik16s Cs6rgO and David M. Mason initiated their collaboration on
the topics of this book while attending the CBMS-NSF Regional
Confer ence at Texas A & M University in 1981. Independently of
them, Sandor Cs6rgO and Lajos Horv~th have begun their work on this
subject at Szeged University. The idea of writing a monograph
together was born when the four of us met in the Conference on
Limit Theorems in Probability and Statistics, Veszpr~m 1982. This
collaboration resulted in No. 2 of Technical Report Series of the
Laboratory for Research in Statistics and Probability of Carleton
University and University of Ottawa, 1983. Afterwards David M.
Mason has decided to withdraw from this project. The authors wish
to thank him for his contributions. In particular, he has called
our attention to the reverse martingale property of the empirical
process together with the associated Birnbaum-Marshall inequality
(cf.,the proofs of Lemmas 2.4 and 3.2) and to the Hardy inequality
(cf. the proof of part (iv) of Theorem 4.1). These and several
other related remarks helped us push down the 2 moment condition to
EX < 00 in all our weak approximation theorems.
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