Talk:Krein–Milman theorem

Untitled
I managed to get a scan of the original Krein–Milman paper from the net, and consequently changed the reference back to the correct title. Yes, that paper does indeed say “regular convex”, while the MR entry on Milman's 1947 paper says “regularly convex”. Just one of life's oddities.

I thought Milman's converse and Choquet's theorem belonged here, so I put them in. An accessible reference for the former would be nice.

Personally, I'd be tempted to skip the biographical factlets on David Milman, as he does in fact have his own wikipedia page. But since I am new to this, I'll not stick my neck that far out (yet).

Hanche 22:55, 31 January 2007 (UTC)


 * I agree that the bio of Milman is out of place here. I removed it Oleg Alexandrov (talk) 03:07, 1 February 2007 (UTC)

Bad idea: State your assumptions in full
In the section titled Related results, the first sentence begins as follows:

"Under the previous assumptions on K if T is a subset of K and the closed convex hull of T is all of K ...."

It is an extremely bad idea, in a Wikipedia math article, not to state the assumptions being used right at the place where they are being used.

In this case, various assumptions were made on K — but not even in the same or the previous section but two sections back. Even if the intended assumptions were unambiguous, someone is likely to change that section in the future, leaving the later section unclear.

So: State assumptions where they are used. (Unless of course there is a continuous block of text, clear to the reader, that uses the same assumptions.)108.245.209.39 (talk) 00:31, 20 July 2018 (UTC)

Weaker assumption on the space
In the book "Functional analysis and semi-groups" by Hille and Phillips it is stated (Section 2.6) that the local convexity assumption can be weakened to the following one: For each non-zero element of the space there exists a continuous linear functional (i.e. an element of the topological dual) that is non-zero on this element. — Preceding unsigned comment added by 92.74.56.210 (talk) 18:22, 11 December 2019 (UTC)