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The purpose of this note is to present an anisotropic variant of the BMO-type norm introduced in  and to show its relation with a surface measure, which is indeed a multiple of the perimeter in the isotropic case. This is done in the spirit of the new characterization of the perimeter of a measurable set in recently studied by Ambrosio, Bourgain, Brezis and Figalli in .
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Giovanni E. Comi, <i>BMO</i>-type norms and anisotropic surface measures. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 3, pp. 431–437DOI 10.4171/RLM/815