A remark on absolutely continuous functions in IR^n

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Abstract

We introduce the notion of α, λ-absolute continuity for functions of several variablesand we compare it with the Hencl’s definition. We obtain that each α,λ-absolutelycontinuous function is n, λ-absolutely continuous in the sense of Hencl and hence iscontinuous, differentiable almost everywhere and satisfies change of variables resultsbased on a coarea formula and an area formula.
Original languageEnglish
Pages (from-to)296-304
JournalRendiconti del Circolo Matematico di Palermo
Volume55
Publication statusPublished - 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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