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When is f(x_1, x_2, . . ., x_n)=u_1(x_1)+u_2(x_2)+ . . . +u_n(x_n)?

A. Klopotowski·M. G. Nadkarni·K. P. S. Bhaskara Rao
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Abstract

We discuss subsets $S$ of ${\mathbb{R}}^n$ such that every real valued function $f$ on $S$ is of the form {equation*} f(x_1,x_2,...,x_n) = u_1(x_1) + u_2(x_2) + ... + u_n(x_n), {equation*} and the related concepts and situations in analysis.

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A. Klopotowski, M. G. Nadkarni, K. P. S. Bhaskara Rao. 2003-12-05. When is f(x_1, x_2, . . ., x_n)=u_1(x_1)+u_2(x_2)+ . . . +u_n(x_n)?. https://arxiv.org/abs/math/0312122

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