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5 May 2004: Finally, suppose that the average of f is significantly higher over A than it is over B. ... This probability increases with t, and the increase is very considerable when t is a couple of standard deviations higher than the average of f over B.

21 Oct 2004: Consider the space Mn of n n matrices over C with theoperator norm. ... j=1. |G(xj) G(xj1)|. where the supremum is taken over all possible dissections.Suppose f : [a,b] R is continuous.

20 Oct 2004: in symbolic form. (For this question the letters m, n, a, b should be understood as ranging. ... over all positive integers - for instance, m really means m N.).

13 Nov 2004: 1 λ1 = inff. G-var f. var f,. where the infimum is taken over all non-constant f : V (G) R. ... Multiplying both side by |Xi||Xj|N 2. and summing over all (i, j),splitting into a sum over I and a sum over Ic, we have.

16 Nov 2004: Theorem 67 (Euclidean division) If a and b are polynomials over a fieldF and b 6= 0 then we can find polynomials q and r such that a = qb r andr < ... n1 1 over Zp for some prime p and some integer n 1.