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2013 | 1 | 295-301
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The Lusin Theorem and Horizontal Graphs in the Heisenberg Group

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In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an application we construct surfaces in the Heisenberg group with tangent spaces being horizontal a.e.
  • Department of Mathematics, University of Pittsburgh,
    301 Thackeray Hall, Pittsburgh, PA 15260, USA,
  • Department of Mathematics, University of Pittsburgh,
    301 Thackeray Hall, Pittsburgh, PA 15260, USA,
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