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We introduce a maximal operator N, which coincides with the maximal Hardy-Littlewood operator if \\mu(B(x,r))\\approx r^n for x\\in\\supp(\\mu), and we show that all n-dimensional Calderon-Zygmund operators are bounded on L^p(w d\\mu) if and only if N is bounded on L^p(w d\\mu), for a fixed p\\in(1,\\infty). 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Let \\mu be a Borel measure on \\R^d which may be non doubling. The only condition that \\mu must satisfy is \\mu(B(x,r))\\leq Cr^n for all x\\in\\R^d, r>0 and for some fixed n with 0<n\\leq d. We introduce a maximal operator N, which coincides with the maximal Hardy-Littlewood operator if \\mu(B(x,r))\\approx r^n for x\\in\\supp(\\mu), and we show that all n-dimensional Calderon-Zygmund operators are bounded on L^p(w d\\mu) if and only if N is bounded on L^p(w d\\mu), for a fixed p\\in(1,\\infty). 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