, is equivalent to ?(? ?1 (? X (B(., ?) ? D 0 ))). We observe that D 0 ? B(y, ?) ? B(y, ?). Therefore, we have ?(A ? (y)) = ?(? ?1 (? X (B(y, ?)))) ? ?, OF THE CONVERGENCE IN DISTRIBUTION We have to prove that ?(A ? (.))

, We recall that (x, s) ? g s (x) is a C 1 -diffeomorphism of X R on its image which contains the ball B(y, ?), assuming ? is sufficiently small

, ?))). Let us consider the point z ? = g h(z) (?(z)) ? D 0 \ B(y, ?). The diameter of A ? (y) is bounded by C y ? and g t is C 1

, there exists s ? (?h(z), R(z) ? h(z)) such that z" = g s (z ? ) ? B(y, ?)

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