Talk:Cylinder set measure

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In the section: "Cylinder set measures on Hilbert spaces" it says that the measure of a ball of radius r in an n-dimensional Hilbert space tends to 0 as n tends to infinity. This is not obvious - explain it. Leocat 16 Oct 2006

[edit] Cylinder set

This article doesn't link to cylinder set, and appears to use a completely different notation for what is the same idea. I suggest some work to make these two articles more coherent with respect to one another. I slapped a "mergewith" tag on this article; I'm not sure it needs to be merged, but at least some comoonality between the two should be introduced. linas 23:49, 25 October 2006 (UTC)

I agree that some commonality would be nice, but a full merge would be overkill. We should keep the articles separate for the same reason that we have different articles for Borel set and Borel measure: one concept uses the other, but the two benefit from separate consideration. In my opinion, the notation in cylinder set needs a clean-up first (a few missing indices), then we can talk on the cylinder set measure page about how a CSM effectively "measures" the preimages of Borel sets under the finite-dimensional projections, and these preimages are "cylinder sets". Sullivan.t.j 09:36, 26 October 2006 (UTC)
I'll try to uniformize the two articles in a few days, (If don't get distracted). This article would benefit from a slightly simpler example at the start; at the moment, it gives the most general definition up front, which makes it a bit daunting. I'll try my hand at a simplified, low-brow presentation (...If I don't get distracted ...). linas 23:38, 26 October 2006 (UTC)
Never mind. My remarks above were some sort of knee-jerk reaction to my skimming this article. When I set down to read this article, it seemed fine. I think it would be nice to link it to dual space, which has a discussion of continuous-linear as opposed to algebraic linear.linas 22:51, 27 October 2006 (UTC)

[edit] Consistency condition

Question: the article states that a consistency condition is required for projections; the condition states that the measure on a projection is a pushforward. Its not clear to me if is is really a "consistency condition", or whether this is just a general statement along the lines of "gee, pushforwards induce cylinder set measures". If ts really a true "consistency condition", I can only imagine that its some sort of strange way of saying that cylinder set measures must be infinite-dimensional fiber products or something like that? Not sure how to understand this. linas 22:51, 27 October 2006 (UTC)

Never mind, I think I get it, although its a bit opaque still. linas 23:26, 27 October 2006 (UTC)

[edit] Gaussian orthogonal ensemble

I am *very far* from being knowledgable on this topic, but it seems to me that the "canonical Gaussian cylinder set measure" is just the Gaussian orthogonal ensemble ? Or am I confused? Removing the condition that the functionals are over the reals, then one gets the Gaussian unitary ensemble, right? I haven't really thought about this at all, just another knee-jerk on skimming this. linas 22:51, 27 October 2006 (UTC)