Geodesic
Continuity of monotone functions
Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 1-4

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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 $R^n$.
Classification : 26B05, 26B12, 26B15
Keywords: order monotone functions on euclidean spaces; solid set; solid cover; continuity; Lebesgue measure 
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Lavrič, Boris. Continuity of monotone functions. Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 1-4. http://geodesic.mathdoc.fr/item/ARM_1993__29_1-2_a1/