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What is a continuous extension? - Mathematics Stack Exchange
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 …
What's the difference between continuous and piecewise …
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 …
Difference between continuity and uniform continuity
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 but not uniformly …
Continuity and Joint Continuity - Mathematics Stack Exchange
Jan 13, 2012 · the difference is in definitions, so you may want to find an example what the function is continuous in each argument but not jointly
probability theory - Why does a C.D.F need to be right-continuous ...
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 …
Understanding Lipschitz Continuity - Mathematics Stack Exchange
Jul 28, 2017 · I have heard of functions being Lipschitz Continuous several times in my classes yet I have never really seemed to understand exactly what this concept really is. Here is the …
Differentiability implies continuity - A question about the proof
Jun 6, 2015 · Assume the function is continuous at x0 x 0 Show that, with little algebra, we can change this into an equivalent question about differentiability at x0 x 0. With this little bit of …
Why Do We Care About Hölder Continuity? - Mathematics Stack …
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 …
Continuity from below and above - Mathematics Stack Exchange
It's reasonable for a continuous increasing function f with real values, defined on the real line, to have f(tn) ↑ f(t) when tn ↑ t and f(tn) ↓ f(t) when tn ↓ t. As a measure can take possibly infinite …
notation - Different types of sample spaces in probability ...
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 …
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