The Lebesgue Measure of the Algebraic Difference of Two Random Cantor Sets
نویسندگان
چکیده
In this paper we consider a family of random Cantor sets on the line. We give some sufficient conditions when the Lebesgue measure of the arithmetic difference is positive. Combining this with the main result of a recent joint paper of the second author with M. Dekking we construct random Cantor sets F1, F2 such that the arithmetic difference set F2 − F1 does not contain any intervals but Leb(F2 − F1) > 0 almost surely, conditioned on non-extinction.
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