By Shlens J.

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3). 6) and the fact that | Y(s + h) - Y(s)| = |SJ g M n , we have Now Y(t) is continuous in t, and hence the last term here goes to 0 as « -» oo. 3) with Kl = I + 3- 4*K. 1 in asymptotic form. We say a sequence {Y n } of random functions has asymptotically independent increments if the difference goes to 0 for disjoint intervals [s;, tj. 2. Suppose that {Yn} has asymptotically independent increments, that {Yl(t):n = 1, 2, • • •} is uniformly integrable for each t, and that E{ Yn(t)} -» 0 and E{ Y*(t)} -»t as n -» oo for each t; suppose finally that the distributions of the Yn are tight.

6. R. R. CORNWALL, The approximation of perfect competition by a large, but finite, number of traders. ROY O. DA VIES, A non-Prokhorov space. ALEJANDRO D. DE ACOSTA, Existence and convergence of probability measures in Banach spaces, Trans. Amer. Math. , 152 (1970), pp. 273-298. R. M. , 27 (1966), pp. 251-268. Distances of probability measures and random variables, Ann. Math. , 39 (1968), pp. 1563-1572. VACLAV FABIAN, On uniform convergence of measures, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 15 (1970), pp.

14) for the general case follows by a passage to the limit. 13) satisfies By stationarity, whence follows the uniform integrability of the mn. 3. M), where

### A tutorial on Principal Component Analysis by Shlens J.

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