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A condition for monotony

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Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 123))

Abstract

The following is a classical theorem, given (for instance) in Titchmarsh’s “Theory of Functions” (2nd edition, 1938), p. 370 Lemma 2: If f(x) is continuous in (a, b) and D + f ≥ 0 almost everywhere therein, and D+ f > −∞ everywhere, then f is non-decreasing.

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© 1997 Springer Basel AG

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Love, E.R. (1997). A condition for monotony. In: Bandle, C., Everitt, W.N., Losonczi, L., Walter, W. (eds) General Inequalities 7. ISNM International Series of Numerical Mathematics, vol 123. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8942-1_32

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  • DOI: https://doi.org/10.1007/978-3-0348-8942-1_32

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9837-9

  • Online ISBN: 978-3-0348-8942-1

  • eBook Packages: Springer Book Archive

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