Oct 15, 2016 · A piecewise continuous function doesn't have to be continuous at finitely many points in a finite interval, so long as you can split the function into subintervals such that each …

May 10, 2019 · This fact is useful to resolve this natural question: Let $\{X_i\}_{i=1}^{\infty}$ be i.i.d. random variables uniform over $[-1,1]$.

Jan 27, 2014 · I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions. …

The following is worth pointing out: Firstly, note that if we replace "continuous" with "differentiable", the new statement isn't true.

Added @Dimitris's answer prompted me to mention, beyond the fact that the implication on normed spaces indeed is an equivalence, that it's the converse which holds in the wider …

{Differentiable functions} $\subset$ {Continuous functions} $\subset$ {Integrable functions} i.e., each is a proper subset of the next. Now, "Differentiable functions set" is a proper subset of …

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Aug 15, 2016 · Definition Continuous function. Let f be a function whose domain is the x axis or is made up of open intervals. Then f is a continuous function if it is continuous at each number a …

Nov 14, 2012 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Jun 12, 2016 · Are continuous functions on those sets uniformly continuous? Can you remember any theorems regarding those? Another idea is to start to try to prove the statement and see …