<A HREF="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.155.4899&rep=rep1&type=pdf">Probability: Theory and Examples</A>, R. Durrett (2010), chapter 8. <A HREF="http://store.elsevier.com/product.jsp?isbn=9780121741518">A course in probability theory</A>, K.L. Chung (2000). From a <A HREF="http://www.ams.org/journals/bull/1969-75-04/S0002-9904-1969-12251-2/S0002-9904-1969-12251-2.pdf">review</A> of Chung's book: > There is a substantial chapter on > invariance theorems, including > Donsker's invariance principle, the > Doob-Donsker proof of the > Kolmogorov-Smirnov theorem and finally > a general invariance principle of > Skorokhod, the proof of which is only > sketched. ------------ for Donsker's theorem in the context of more general metric spaces, see: <A HREF="http://www.amazon.com/dp/0471197459/ref=rdr_ext_tmb">Convergence of Probability Measures</A>, by P. Billingsley (1999)