Approximation of Lebesgue Integrals by Riemann Sums and Lattice Points in Domains with Fractal Boundary
نویسندگان
چکیده
Sets thrown at random in space contain, on average, a number of integer points equal to the measure of these sets. We determine the mean square error in the estimate of this number when the sets are homothetic to a domain with fractal boundary. This is related to the problem of approximating Lebesgue integrals by random Riemann sums.
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