Talk:Cylinder set measure

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
thread_title:  [[Cylinder set]] 

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

message: 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)
thread_title: Gaussian orthogonal ensemble

message: The title says it all! This article uses the concept "quotient inner product" on a Hilbert space, but it is not defined, as far as I can see. Kjetil Halvorsen 01:56, 31 March 2011 (UTC)
replies: text: I assume its just the pushforward. 67.198.37.16 (talk) 20:38, 30 September 2020 (UTC)
thread_title:  What is "quotient inner product"?