The continuous extension of f(x) at x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on "continuous extension" throughout …

May 10, 2019 · In an alternative history, c.d.f.'s might have been defined as P a P ω Ω X ω a with strict inequality, and then these functions would be continuous from the left rather than from …

Aug 4, 2022 · So, there will be a discontinuity at time k. Isn't this violating the definition of continuous stochastic process or is it that I have to keep ω ω constant throught out the …

Jan 27, 2014 · To understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on R R but not uniformly …

Oct 8, 2021 · Hölder continuous functions do not give rise to useful weak solutions in any context I am aware of: there are notions of weak solutions that are continuous, but the Hölder modulus …

Are there any examples of functions that are continuous, yet not differentiable? The other way around seems a bit simpler -- a differentiable function is obviously always going to be continuous.

Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a …

May 29, 2016 · In any such branch, the complex logarithm is analytic and therefore continuous on the negative real half-line. To conclude, the answer to your question is that xx x x is always …

Oct 22, 2017 · Continuous Models : Probabilistic models with continuous sample spaces differ from their discrete counterparts in that the probabilities of the single-element events may not …

Say I have two topological spaces given by (X, TX) and (Y, TY) where Y is Hausdorff. In addition say I have a function f: X → Y, and let it be continuous. I want to show that Gr(f): = {(x, f(x)) ∣ x …