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 …

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). …

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 …

Dec 16, 2023 · The theorems about the Lebesgue integral require only pointwise convergence + some other condition. Actually, this is one of the main advantages of Lebesgue integration …

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 $x$, …

Perhaps the problem is that you are only given a subsequence which converges almost everywhere, and there are uncountably many such sequences (so the total problem area …

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!

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. …