Abstract
This chapter discusses measure of exceptional minimal sets of codimension one foliations. Because the Godbillon measure is absolutely continuous with respect to the usual Lebesgue measure, an exceptional minimal set fails to support the Godbillon measure if it has zero Lebesgue measure. If M is a closed manifold and F is a codimension one Cr foliation on M, then a subset S of M is called a minimal set of F if S is closed, saturated and minimal with respect to inclusions. A minimal set S is called exceptional in case S is neither a single leaf nor the whole manifold M; S is then perfect and without interior. Locally, it is the Cartesian product of a leaf of F and a Cantor set.
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