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I'm removing this example, added by anon some months ago:
I'm removing it because I can't figure out what its trying to say. I think C[0,1] is supposted to be the set of all discrete-time stochastic processes, or something like that; not sure. The union also does not make sense. linas 21:18, 27 October 2006 (UTC)
On this page I read,
Consider the cartesian product of topological spaces , indexed by some index . The canonical projection is the function that selects out the component of the product. Then, given any open set , the preimage is called an open cylinder.
Where the definition of open set is members of a topology. So is any collection of these open sets (i.e. U) also an open set? is there some property U must have to be an open set? Is it not the same definition as I stated? PDBailey ( talk) 02:51, 22 January 2009 aka O18 ( talk)
The article is focused on cylinder sets in a product topology, while they play an important role also in a product sigma-algebra, at least in the countable case. I think the article should deal with the two concepts equally. Markov Odometer ( talk) 06:18, 22 March 2018 (UTC)
For the TODO List: The article abstract Wiener space provides a definition of cylinder sets on Hilbert spaces that is slightly more general than the definitions in this article. Articulation would be beneficial.
Also, this article should start not with the general definition, but with a simple motivating example. 67.198.37.16 ( talk) 18:16, 29 January 2024 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
I'm removing this example, added by anon some months ago:
I'm removing it because I can't figure out what its trying to say. I think C[0,1] is supposted to be the set of all discrete-time stochastic processes, or something like that; not sure. The union also does not make sense. linas 21:18, 27 October 2006 (UTC)
On this page I read,
Consider the cartesian product of topological spaces , indexed by some index . The canonical projection is the function that selects out the component of the product. Then, given any open set , the preimage is called an open cylinder.
Where the definition of open set is members of a topology. So is any collection of these open sets (i.e. U) also an open set? is there some property U must have to be an open set? Is it not the same definition as I stated? PDBailey ( talk) 02:51, 22 January 2009 aka O18 ( talk)
The article is focused on cylinder sets in a product topology, while they play an important role also in a product sigma-algebra, at least in the countable case. I think the article should deal with the two concepts equally. Markov Odometer ( talk) 06:18, 22 March 2018 (UTC)
For the TODO List: The article abstract Wiener space provides a definition of cylinder sets on Hilbert spaces that is slightly more general than the definitions in this article. Articulation would be beneficial.
Also, this article should start not with the general definition, but with a simple motivating example. 67.198.37.16 ( talk) 18:16, 29 January 2024 (UTC)