We introduce the notion of α, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that each α,λ-absolutely continuous function is n, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change of variables results based on a coarea formula and an area formula.
DI BARI C, VETRO C (2006). A remark on absolutely continuous functions in IR^n. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 55, 296-304.
A remark on absolutely continuous functions in IR^n
DI BARI, Cristina;VETRO, Calogero
2006-01-01
Abstract
We introduce the notion of α, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that each α,λ-absolutely continuous function is n, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change of variables results based on a coarea formula and an area formula.
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