The continuous extension of f(x) f (x) at x = c 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" …

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 …

May 10, 2019 · This function is always right-continuous. That is, for each x ∈ Rk x ∈ R k we have lima↓xFX(a) =FX(x) lim a ↓ x F X (a) = F X (x). My question is: Why is this property important? …

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 …

Dec 28, 2015 · A continuous random variable is a random variable with a continuous cumulative distribution function F F. Typically the range of a continuous random variable is R R, [0, ∞) [0, …

In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?

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

As you have it written now, you still have to show x−−√ x is continuous on [0, a) [0, a), but you are on the right track. As @user40615 alludes to above, showing the function is continuous at …

Jan 24, 2015 · A continuously differentiable function f(x) f (x) is a function whose derivative function [Math Processing Error] f (x) is also continuous at the point in question.

Apr 16, 2023 · Here instead of starting with the Lp L p space and selecting continuous elements, we had to complete the space of continuous functions on the boundary formed by the …