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Oct
23
comment Borel Measure is Outer Regular iff it is inner regular?
@GEdgar, I did! Writing down the definition of outer regular and inner regular is the basic starting of the proof. The question I am seeking is the conclusion part of the theorem "iff it is inner regular". I am well aware too that each Borel subset of the compact space satisfy both definition but from my understanding of this theorem, we need to show it is inner regular first then only outer regular which I am not sure I am right and am lost.
Oct
23
comment Borel Measure is Outer Regular iff it is inner regular?
Anyone can shed some light on this question?
Oct
22
comment Borel Measure is Outer Regular iff it is inner regular?
I am not sure, GEdgar. I found this information from Bauer's book under Measures on Topological Spaces and am still thinking.
Oct
22
asked Borel Measure is Outer Regular iff it is inner regular?
Aug
15
accepted Distinction between Directed System and Directed Set
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14
asked Distinction between Directed System and Directed Set
Jan
10
comment Function that is not differentiable at a point
I am looking for a function which like two lines meet at one point and its not differentiable there. For $x^{2}$, its just like one sided line only although it is symmetrical.
Jan
10
comment Function that is not differentiable at a point
That is true. I am trying to show Paul du Bois-Reymond work from 1876 that says continuous function whose Fourier series diverge at a point. At present even reviewing all the available journal, there is no such function stated anywhere except proofs given by various authors that based on partial sums if I remember correctly.
Jan
10
comment Function that is not differentiable at a point
From the graph of this function, I can't explain about the one point I need. I am trying to explain about the convergence and hence differentiability at one point just like $\vert x \vert$. I have even look through Handbooks of Mathematics & Tables and integrals reference books but to no avail.
Jan
10
comment Function that is not differentiable at a point
Yes I had plotted $\vert x \vert$ as one of my example. I am looking for another one with the same value at $(-\pi,\pi)$ and had more worst differentiability at a point than $\vert x \vert$. The one I gave in my first post had a very bad differentiability at $x=0$ but too bad even Mathematica can't draw out its partial sums.
Jan
10
comment Function that is not differentiable at a point
@AymanHourieh - Yes I had done this. Thank you. I am looking for one other example.
Jan
10
comment Function that is not differentiable at a point
This is the $a_{n}$ computed by Mathematica => $\frac{(\pi BesselJ[1, (\frac{n\pi}{2}] \cos \frac{n \pi}{2}}{n}$. When plotting it as a graph, Mathematica can't continue.
Jan
10
comment Function that is not differentiable at a point
@Ilya - Yes I did using Mathematica. When plotting the $a_{n}$, even Mathematica produced an error saying exceed limit, etc and couldn't continue. This equation took about 40 mins to be process by Mathematica on my computer.
Jan
10
asked Function that is not differentiable at a point