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I managed to get a scan of the original KreinâMilman paper from the net, and consequently changed the reference back to the correct title. Yes, that paper does indeed say âregular convexâ, while the MR entry on Milman's 1947 paper says âregularly convexâ. 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)
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 â 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)
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. â Preceding unsigned comment added by 92.74.56.210 ( talk) 18:22, 11 December 2019 (UTC)
This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
I managed to get a scan of the original KreinâMilman paper from the net, and consequently changed the reference back to the correct title. Yes, that paper does indeed say âregular convexâ, while the MR entry on Milman's 1947 paper says âregularly convexâ. 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)
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 â 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)
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. â Preceding unsigned comment added by 92.74.56.210 ( talk) 18:22, 11 December 2019 (UTC)