There are other ways a function can be a continuous extension, but probably the most basic way (and likely about the only way you'll see in elementary calculus) is that you have a function …

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 $[-1,1]$.

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 …

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. …

This is also how Weierstrass' famous continuous everywhere, differentiable nowhere function was proven to ...

A natural class of examples would be paths of Brownian motion. These are continuous but non-differentiable everywhere. You may also be interested in fractal curves such as the Takagi …

$\begingroup$ @user135626: What I wrote is correct. You are misreading it. I'm not saying the derivative is zero, I'm saying that if the derivative exists, the numerator of the difference …

Aug 4, 2022 · Isn't this violating the definition of continuous stochastic process or is it that I have to keep $\omega$ constant throught out the process ? Also, is $\omega$ in the definition of …

Prove that if $ f $ is continuous on $ \left[ 0, \infty\right)$ and uniformly continuous on $[b, \infty ...

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 …