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On some problem of A. Rosłanowski
We present a negative answer to problem 3.7(b) posed on page 193 of  , where, in fact, A. Ros lanowski asked: Does every set of Lebesgue measure zero belong to some Mycielski ideal ? We identify a set X ∈ [ω] ω with its characteristic function, i.e. with the sequence (X(0), X(1), . . .) ∈ 2 ω such that X(n) = 1 iff n ∈ X. A set X ∈ [ω] ω has asymptotic density d whenever where |X ∩ n| denotes the number of natural numbers from X less than n. We consider the family of all sets of asymptoticdoi:10.4064/cm-69-2-297-298 fatcat:plwnsh2ybnamfosmcrye3neasq