Jim writes: << Can anyone find an explicit construction of an infinite sequence S of 0's and 1's with the property that for any finite bit-string s, the relative frequency with which s occurs in the first N bits of S converges to (1/2)^(length of s) with error that falls like (log N)/N?

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May I ask for a clarification of exactly what "error that falls like (log N)/N" means? I think I know what this means, but would like to see the condition expressed in formal language, just to be certain. --Dan