Definition For Vector Spaces
Given a finite or infinite-dimensional vector space over a field K (such as the real or complex numbers), the cylinder sets may be defined as
where is a Borel set in, and each is a linear functional on ; that is, the algebraic dual space to . When dealing with topological vector spaces, the definition is made instead for elements, the continuous dual space. That is, the functionals are taken to be continuous linear functionals. The article on dual spaces discusses the differences between the algebraic and the continuous dual spaces.
Read more about this topic: Cylinder Set
Famous quotes containing the words definition and/or spaces:
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“Deep down, the US, with its space, its technological refinement, its bluff good conscience, even in those spaces which it opens up for simulation, is the only remaining primitive society.”
—Jean Baudrillard (b. 1929)