Talk:Borel–Carathéodory theorem

Question about the proof
Why is $$|f(z)-2A| \ge |f(z)|$$ for $$|z| = R$$? Note that A is defined as the supremum over the disc with radius r < R. -- Jitse Niesen (talk) 13:20, 6 September 2005 (UTC)


 * That's really the triangle inequality, in the form under Consequences on that page, isn't it? Charles Matthews 16:08, 6 September 2005 (UTC)

I can see that $$|f(z)-2A| \ge |f(z)|$$ if |z| = r, but not if |z| = R. -- Jitse Niesen (talk) 16:40, 6 September 2005 (UTC)

Now fixed. It turns out the statement of the theorem was wrong. -- Jitse Niesen (talk) 18:23, 15 September 2005 (UTC)

Revised proof
Frankly, when I came to this page, I hated the proof. It was utterly unmotivated and had badly chosen trivial details thrown in that would be second nature to anyone able to understand the proof in the first place. It seemed to have been lifted almost entirely from Lang, which is better written but still unmotivated. Unfortunately, it seems Lang's presentation is common--the only other source I found is a very slight rearrangement.

That said, I spent some time finding the intuition behind the proof, which is actually really simple. Along the way I streamlined this article's proof and, most importantly, motivated the seemingly inspired choice of auxiliary function. Unfortunately, I don't have a source for any of these changes, since I made them up this evening. The result is, IMO, cleaner, quicker, and much clearer than Lang and its derivatives. Hopefully that's not a problem? The spirit of Lang's proof remains, for what it's worth. — Preceding unsigned comment added by 50.132.8.186 (talk) 07:39, 3 August 2013 (UTC)
 * Sure, kindly, stay in touch with the page. InfocenterM (talk) 07:43, 3 August 2013 (UTC)