Definition:Oscillation/Real Space/Oscillation at Point/Limit
< Definition:Oscillation | Real Space | Oscillation at Point(Redirected from Definition:Oscillation of Real Function at Point/Limit)
Jump to navigation
Jump to search
Definition
Let $f: X \to Y$ be a real function.
Let $x \in X$.
The oscillation of $f$ at $x$ is defined as:
- $\ds \map {\omega_f} x := \lim_{h \mathop \to 0^+} \map {\omega_f} {\openint {x - h} {x + h} \cap X}$
where $\map {\omega_f} {\openint {x - h} {x + h} \cap X}$ denotes the oscillation of $f$ on $\openint {x - h} {x + h} \cap X$.
Sources
- 2010: J.N. Sharma and A.R. Vasishta: Mathematical Analysis-II: Chapter $6$, $\S 7$: Saltus at a point