Lipschitz maps and nets in Euclidean space
نویسنده
چکیده
for x 6= x′. A set Y ⊂ Rn is a net if there is an R such that d(x, Y ) < R for every x ∈ Rn; it is separated if there is an ǫ > 0 such that |y − y′| > ǫ > 0 for every pair y 6= y′ in Y . History. In 1965, J. Moser showed that any two positive, C∞ volume forms on a compact manifold with the same total mass are related by a diffeomorphism [Mos]. Extensions of this result to other smoothness classes such as Ck,α were given in [Rei1] and [DM]; see also [RY1], [RY2], and [Ye].
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