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Additional info for An Intro. to Differential Geometry With Applns to Elasticity

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A. x E II -L. In order to state our main results we need the following notation. For fJ E M+(lR n ), mE {I, ... ,n} and II E G(n, m) write bJ-'(q) = bJ-'(q) - bHn-rnLITl- (q) = bJ-'(q) - (n - m)(l - q), Ct . - miD - qmin -- { q < 0 I - sup _ O

In Aspects of Mathematics and its Applications, ed. J. A. Barroso, Elsevier Science Publishers B. , (1986), 419-430. -P. Kahane, Positive Martingales and Random Measures. Chinese Ann. Math. 8b (1987),1-12. -P. Kahane, Multiplications aleatoires et dimensions de Hausdorff. Ann. Inst. Poincare 23 (1987), 289-296. -P. Kahane. Random multiplications, random coverings, and multiplicative chaos. Analysis at Urbana, Proceedings of the Special Year in Modern Analysis at the University of Illinois, 1986-87 (editors E.

I) The Fourier transform S(~) = I~CXl eit €. 1 ) n=O and this formula has been crucial for number-theoretic considerations. (ii) v).. (x) = v).. (x) = 2"1[F).. (X-I) -,X- + F).. (X+l)] -,X- . 1991 Mathematics Subject Classification. Primary 42A85; Secondary HR06, 26A46, 26A30, 28A 78, 28A80 Key words and phrases. self-similar measures, Hausdorff dimension, Salem numbers Research of Peres was partially supported by NSF grant #DMS-9803597. Research of Solomyak was supported in part by NSF grant #DMS 9800786, the Fulbright foundation, and the Institute of Mathematics at the Hebrew University of Jerusalem.

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