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In this chapter, we introduce yet one more kind of representations of the p-adic 1-Lipschitz functions, namely, as plots in Euclidean space: in the unit n-dimensional hypercube \([0,1]^n\) or, when convenient, on the surface of n-dimensional unit torus \(\mathbb T^n\) . Moreover, the representations may at the same time be considered in dual space, as functions on complex characters of \(\mathbb Q_p\) . The representations carry important information about measure properties of 1-Lipschitz functions; the information will be needed in Chaps. 13 and 16 .

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Plots of 1-Lipschitz Functions in Euclidean Space

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  • 发表日期：

    2025年

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  • Vladimir Anashin

摘要

In this chapter, we introduce yet one more kind of representations of the p-adic 1-Lipschitz functions, namely, as plots in Euclidean space: in the unit n-dimensional hypercube \([0,1]^n\) or, when convenient, on the surface of n-dimensional unit torus \(\mathbb T^n\) . Moreover, the representations may at the same time be considered in dual space, as functions on complex characters of \(\mathbb Q_p\) . The representations carry important information about measure properties of 1-Lipschitz functions; the information will be needed in Chaps. 13 and 16 .