Definition:Absolute Continuity/Real Function
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Let $I \subseteq \R$ be a real interval.
A real function $f: I \to \R$ is said to be absolutely continuous if it satisfies the following property:
- For every $\epsilon > 0$ there exists $\delta > 0$ such that the following property holds:
- Results about absolutely continuous functions can be found here.
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: absolutely continuous: 1. (of a real function)
- 2013: Francis Clarke: Functional Analysis, Calculus of Variations and Optimal Control ... (previous) ... (next): $1.1$: Basic Definitions
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: absolutely continuous function