2 mar 2021 -- 14:30 [open in google calendar]
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The classical Lusin theorem states that any measurable function can be approximated by a continuous function except on a set of small measure. Analogous results for higher smoothness give conditions under which a function can be approximated by a Cm function up to a set of small measure. Proving these results depends on applying a suitable Whitney extension theorem. After recalling the classical results in Euclidean spaces, we discuss recent work extending some of these results to Carnot groups. Based on joint work with Andrea Pinamonti and Marco Capolli.