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Article

Lavrič, Boris
Continuity of monotone functions. (English). Archivum Mathematicum, vol. 29 (1993), issue 1, pp. 1-4
MSC: 26B05, 26B12, 26B15 | MR 1242622 | Zbl 0805.26005
Keywords:
order monotone functions on euclidean spaces; solid set; solid cover; continuity; Lebesgue measure
Summary:
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 $R^n$.
References:
[1] Marsden, J. E.: Elementary Classical Analysis. Freeman and Company, San Francisco, 1974. MR 0357693 | Zbl 0285.26005
[2] Spivak, M.: Calculus on Manifolds. Benjamin, New York, 1965. MR 0209411 | Zbl 0141.05403
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