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跳跃间断 定义
A jump discontinuity or step discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another. It is a discontinuity where the limits from the left and right both exist but are not equal to each other. A real-valued univariate function f = f(x) has a jump discontinuity at a point x0 in its domain provided that limx→xa- f(x) = L1 < ∞, and limx→xa+ f(x) = L1 < ∞. both exist and L1 ≠ L2.
跳跃不连续性的概念不应与很少使用的约定相混淆,其中术语 jump 用于定义任何类型的功能性不连续性。虽然在代数上没有 可移动不连续性那么简单,但跳跃不连续性远不如其他类型的奇点(例如无限不连续性)表现不佳。在许多情况下都可以看到这一事实。例如,univariate 单调函数最多可以有许多不连续点,其中最坏的可能是跳跃不连续点。不出所料,上面给出的定义也可以推广到 multivariate 实值函数中的跳跃不连续性。
来源
“Jump Discontinuity.” From Wolfram MathWorld, mathworld.wolfram.com/JumpDiscontinuity.html.