Sam Walters ☕️ a Twitter: "It is known that a sequence of functions that converges pointwise on a space X need not converge uniformly on X. But Egoroff's Theorem says that you
![10. Read through the following "e-free" proof of the uniform convergence of power series. Does it... - HomeworkLib 10. Read through the following "e-free" proof of the uniform convergence of power series. Does it... - HomeworkLib](https://img.homeworklib.com/images/d5c7efcb-89dd-4b68-af67-ee138712386a.png?x-oss-process=image/resize,w_560)
10. Read through the following "e-free" proof of the uniform convergence of power series. Does it... - HomeworkLib
![SOLVED:Tne Fcurier series of f:[ _ T,T] R f(x) = Ixl converges uniformly to since tne Pointwise Convergence theorem applies and f(-T) = f(t). f:[-T,] - R is continuous f(-TT) = f(T) SOLVED:Tne Fcurier series of f:[ _ T,T] R f(x) = Ixl converges uniformly to since tne Pointwise Convergence theorem applies and f(-T) = f(t). f:[-T,] - R is continuous f(-TT) = f(T)](https://cdn.numerade.com/ask_images/1827d7ffa86f4cb6ab93ae1ba1bbb233.jpg)
SOLVED:Tne Fcurier series of f:[ _ T,T] R f(x) = Ixl converges uniformly to since tne Pointwise Convergence theorem applies and f(-T) = f(t). f:[-T,] - R is continuous f(-TT) = f(T)
![On Uniform Convergence in the Wiener‐Wintner Theorem - Arthur Robinson - 1994 - Journal of the London Mathematical Society - Wiley Online Library On Uniform Convergence in the Wiener‐Wintner Theorem - Arthur Robinson - 1994 - Journal of the London Mathematical Society - Wiley Online Library](https://londmathsoc.onlinelibrary.wiley.com/cms/asset/138de7fb-8b7c-403d-8a93-4a0a74d1e6c4/jlms_49.3.493.fp.png)
On Uniform Convergence in the Wiener‐Wintner Theorem - Arthur Robinson - 1994 - Journal of the London Mathematical Society - Wiley Online Library
![real analysis - Question about proof: Uniform cauchy $\Rightarrow$ Uniform convergence - Mathematics Stack Exchange real analysis - Question about proof: Uniform cauchy $\Rightarrow$ Uniform convergence - Mathematics Stack Exchange](https://i.stack.imgur.com/ruUCQ.png)
real analysis - Question about proof: Uniform cauchy $\Rightarrow$ Uniform convergence - Mathematics Stack Exchange
![On the Uniform Convergence of Fourier Series - Morgan - 1936 - Journal of the London Mathematical Society - Wiley Online Library On the Uniform Convergence of Fourier Series - Morgan - 1936 - Journal of the London Mathematical Society - Wiley Online Library](https://londmathsoc.onlinelibrary.wiley.com/cms/asset/d90509e9-e734-4d67-b4b6-460c8f1817dc/jlms_s1-11.3.162.fp.png)