13 февр. 2017 г. · The function that you converge to pointwise isn't continuous, and this always means that the convergence isn't uniform (if each fn is ...

31 июл. 2020 г. · A uniformly convergent series of continuous functions has a continuous sum function. Thus if the sum function is not continuous ...

18 сент. 2017 г. · I will prove that the series is well defined and converges uniformly on compacts on the open set R∖{−1,1}. Let fn(x)=xn1+x2n.

26 янв. 2020 г. · In uniform convergence problems it helps to use worst-case reasoning. Which x values would cause the worst problem for convergence? – kimchi ...

11 сент. 2021 г. · If the fn are continuous but their pointwise limit is not, then convergence is not uniform. Following this advice, you should note that fn(0) ...

21 июн. 2013 г. · For uniform convergence you want fn to be close to f, regardless of x. Here you need to pay attention to behavior of xn. IS it true that ...

29 авг. 2018 г. · If you can always find an x∈[0,1) such that f(x)=1/2, then you can not get closer to 0 than 1/4 uniformly on [0,1).

28 дек. 2020 г. · Checking exercise on uniform convergence and differentiation ; g′n(x)=xn−1 converges pointwise to 0 for ; x∈[0,1) and to 1 for ; x=1, so ...

8 дней назад · The question is as follows: Suppose that (fn) converges to a function f uniformly on D. Prove that if each fn is bounded on D then f is bounded ...

5 июн. 2015 г. · How to draw this matrix with stairs and submatrices? Can a contradiction exist in the antecedent of a sequent? How many colors do we need? What ...