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). …

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 …

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 …

Jul 8, 2019 · I am programming a basic mathematical library that deals with vectors, matrices, tensors, holors, functions, etc. I am wondering what the best terminology will be regarding …

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 …

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!

Jul 29, 2021 · This proof involves rewriting the Fourier Series to its Dirichlet-kernel form, and the Riemann-Lebesgue Lemma is applied to prove pointwise convergence. A proof of the …

This is the common theme for Pointwise convergence problems and is why (in my opinion) we have this definition. To sum up: Uniform convergence is the intuitive definition.

Apr 14, 2022 · I need help to prove the following theorem Suppose $f$ is the pointwise limit of a sequence of $f_n$, $n = 1, 2, \cdots$, where $f_n$ is a Borel measurable function on $X$.

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 …