| 词条 | Cylindrical σ-algebra |
| 释义 |
In mathematics — specifically, in measure theory and functional analysis — the cylindrical σ-algebra is a σ-algebra often used in the study either product measure or probability measure of random variables on Banach spaces. For a product space, the cylinder σ-algebra is the one which is generated by cylinder sets. As for products of countable length, the cylindrical σ-algebra is the product σ-algebra.[1] In the context of Banach space X, the cylindrical σ-algebra Cyl(X) is defined to be the coarsest σ-algebra (i.e. the one with the fewest measurable sets) such that every continuous linear function on X is a measurable function. In general, Cyl(X) is not the same as the Borel σ-algebra on X, which is the coarsest σ-algebra that contains all open subsets of X. See also
References
| last1 = Ledoux | first1 = Michel | last2 = Talagrand | first2 = Michel | author2-link = Michel Talagrand | title = Probability in Banach spaces | publisher = Springer-Verlag | location = Berlin | year = 1991 | pages = xii+480 | isbn = 3-540-52013-9 | mr = 1102015 }} (See chapter 2) 1. ^{{cite book |title=Real Analysis: Modern Techniques and Their Applications |page=23 |chapter= |author=Gerald B Folland |url=https://books.google.com/books?id=wI4fAwAAQBAJ&printsec=frontcover&dq=real+analysis+folland&hl=en&sa=X&ved=0ahUKEwim7vz-uv_ZAhVHr6QKHc3jDuYQ6AEIJjAA#v=onepage&q=real%20analysis%20folland&f=false |isbn=0471317160 |publisher=John Wiley & Sons |year=2013 |edition=}} {{DEFAULTSORT:Cylindrical sigma-algebra}} 2 : Functional analysis|Measure theory |
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