BeDict Logo

oscillation

/ˌɒsɪˈleɪʃən/ /ˌɑːsɪˈleɪʃən/
Visual illustration of oscillation: (of a function) defined for each point x in the domain of the function by \inf\left\{\mathrm{diam}(f(U))\mid U\mathrm{\ is\ a\ neighborhood\ of\ }x\right\}, and describes the difference (possibly ∞) between the limit superior and limit inferior of the function near that point.
noun

(of a function) defined for each point x in the domain of the function by \inf\left\{\mathrm{diam}(f(U))\mid U\mathrm{\ is\ a\ neighborhood\ of\ }x\right\}, and describes the difference (possibly ∞) between the limit superior and limit inferior of the function near that point.