A Class of Self-Affine Sets and Self-Affine Measures

Let I = {φj}j=1 be an iterated function system (IFS) consisting of a family of contractive affine maps on Rd. Hutchinson [13] proved that there exists a unique compact setK = K(I), called the attractor of the IFS I, such that K = ⋃m j=1 φj(K). Moreover, for any given probability vector p = (p1, . . . , pm), i.e. pj > 0 for all j and ∑m j=1 pj = 1, there exists a unique compactly supported probability measure ν = νI,p such that

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