real analysis - Uniform Convergence Implies $L^2 ... math.stackexchange.com › questions › uniform...
14 нояб. 2015 г. · Some of the books that discuss convergence say that uniform convergence implies $L^2$ convergence and $L^2$ convergence implies $L^1$ ... |
26 мар. 2018 г. · It is well known that if a sequence of L2 functions (fn)n∈N converges to a function f, i.e. limn∈N∫‖fn−f‖2dx=0, then there exists a subsequence ... |
27 мар. 2018 г. · To show that fn does not converge pointwise to 0 it is enough to notice that fn(1/2)=1 for all n. |
31 мая 2013 г. · So that means L2 convergence is implied by pointwise convergence? Is it true in infinite measure spaces also? |
19 дек. 2018 г. · If fn→f in L2, then there is a subsequence (fnk), which is pointwise convergent almost everywhere. |
28 сент. 2020 г. · The point is that Ascoli-Arzelá gives uniform convergence of a subsequence to some continuous function, which is completely unknown a priori. |
7 мар. 2018 г. · Prove that, for a sequence of holomorphic functions on a compact set, convergence in L2 implies uniform convergence. |
5 дек. 2022 г. · If I am understanding your question properly, then the answer is no. Consider the sequence of indicator functions fn:=√n1(0,1/n). |
16 мар. 2021 г. · Very roughly, L2 convergence tells you something like that the partial sums converge to the function on average. (Actually, L2 norm convergence ... |
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