 The Hausdorff measure is a generalization of the Lebesgue measure that is useful for measuring the subsets of R"n" of lower dimensions than "n", like submanifolds, for example, surfaces or curves in R3 and fractal sets.The Hausdorff measure is not to be confused with the notion of Hausdorff dimension.It can be shown that there is no infinite-dimensional analogue of Lebesgue measure.