Lipschitz continuity is a stronger property than continuity. First, when I heard this (through Ruediger’s treatment on expectation analysis of codes), it was all haze. For the second time, I made some sense during the Applied Stochastic process course. Anyway, a final appreciation of this concept kicked my brain only when I started working on a problem. Recently, I came across this again and hence thought of penning a few easy lines on this.
Here is a beautiful explanation of this concept.