On Riemann Sums and Lebesgue Integrals.
On the Metric Theory of the Nearest Integer Continued Fraction expansion.
On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II
On strong uniform distribution
On certain solutions of the diophantine equation x-y = p(z)
On a problem of R. C. Baker
On metric diophantine approximation and subsequence ergodic theory.
On strong uniform distribution. IV.
On the Hausdorff dimension of certain self-affine sets
A subset E of ℝⁿ is called self-affine with respect to a collection ϕ₁,...,ϕₜ of affinities if E is the union of the sets ϕ₁(E),...,ϕₜ(E). For S ⊂ ℝⁿ let . If Φ(S) ⊂ S let denote . For given Φ consisting of contracting “pseudo-dilations” (affinities which preserve the directions of the coordinate axes) and subject to further mild technical restrictions we show that there exist self-affine sets of each Hausdorff dimension between zero and a positive number depending on Φ. We also investigate...
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