order monotone functions on euclidean spaces; solid set; solid cover; continuity; Lebesgue measure
It is shown that a monotone function acting between euclidean spaces $R^n$ and $R^m$ is continuous almost everywhere with respect to the Lebesgue measure on $R^n$.
 Marsden, J. E.: Elementary Classical Analysis
. Freeman and Company, San Francisco, 1974. MR 0357693
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