The pointwise convergence depends on each x x, that is you need to count and fix every x x before passing to the limit. On the other hand, uniform convergence is independent of x x.

Is there a notation for element-wise (or pointwise) operations? For example, take the element-wise product of two vectors x and y (in Matlab, x .* y, in numpy x*y), producing a new vector of …

Jul 8, 2019 · When talking vectors/matrices/tensors, pointwise is best avoided because it is decently ambiguous, since vectors can be interpreted as points. So a pointwise multiplication …

The second one is uniform continuity, ive just forgot to change the name (because i copied and modified from the pointwise version). Thanks anyway.

Sep 25, 2015 · Similarly, you could say that vector addition is 'pointwise addition' because you're adding the entries in parallel according to their indices. In the article, rather, it is just using it to …

Apr 21, 2021 · Choosing suitable intervals with length going to zero you can exhibit a sequence of L^p, but pointwise the sequence doesn't converges at any point!

May 14, 2017 · (2) (2) What is the difference between boundedness, pointwise boundedness, and uniform boundedness? (3) (3) If my function is bounded for all x x, does this imply that it is …

Mar 30, 2019 · If fn → f f n → f pointwise, f f is continuous and f f is continuous, then fn → f f n → f uniformly. Ask Question Asked 6 years, 9 months ago Modified 4 years, 11 months ago

Jun 16, 2015 · I need help to prove the following theorem Suppose f f is the pointwise limit of a sequence of fn f n, n = 1, 2, ⋯ n = 1, 2,, where fn f n is a Borel measurable function on X X. Then …

Oct 5, 2013 · Affine functions are themselves concave (and convex). The pointwise infimum of concave functions is concave. You will probably find more for the equivalent: The pointwise …