Hajłasz, Piotr; Kinnunen, Juha Hölder quasicontinuity of Sobolev functions on metric spaces. (English) Zbl 1155.46306 Rev. Mat. Iberoam. 14, No. 3, 601-622 (1998). Summary: We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of J. Malý [Potential Anal. 2, No. 3, 249–254 (1993; Zbl 0803.46037)] to the Sobolev spaces on metric spaces [P. Hajłasz, Potential Anal. 5, No. 4, 403–415 (1996; Zbl 0859.46022)]. Cited in 41 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 28A15 Abstract differentiation theory, differentiation of set functions Citations:Zbl 0803.46037; Zbl 0859.46022 PDF BibTeX XML Cite \textit{P. Hajłasz} and \textit{J. Kinnunen}, Rev. Mat. Iberoam. 14, No. 3, 601--622 (1998; Zbl 1155.46306) Full Text: DOI EuDML OpenURL