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 …

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 …

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

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 where we don't …

Sep 25, 2015 · For the math term of projection Wikipedia links to "function composition", whose page in turn links to "pointwise". The question is: What is “pointwise”, in the context of function composition?

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 …

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 over Riemann …

Jul 25, 2021 · Intuitively I feel like that weak convergence only controls the behavior of integral (by Riesz Representation Theorem), which cannot affect pointwise structure. But I don't know how to construct …

May 28, 2020 · Pointwise convergence does not say much, because most of the important things (derivative, integral, continuity) requires uniform convergence. There is one example I can think of …