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 same ...

Pointwise convergence means at every point the sequence of functions has its own speed of convergence (that can be very fast at some points and very very very very slow at others). Imagine …

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

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 mean that …

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 might just be …

Everywhere pointwise convergence is necessary to guarantee that fn → f f n → f pointwise if every subsequence has a further subsequence which converges to f f pointwise. With that being said, this …

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

Apr 21, 2021 · Commented Apr 28, 2012 at 14:10 1 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!

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 f f …

L1 L 1 convergence gives a pointwise convergent subsequence Ask Question Asked 11 years, 10 months ago Modified 9 years, 7 months ago