Inmathematics — specifically, in measure theory and functional analysis — the cylindrical σ-algebra[1]orproduct σ-algebra[2][3] is a type of σ-algebra which is often used when studying product measuresorprobability measuresofrandom variablesonBanach spaces.
For a product space, the cylinder σ-algebra is the one that is generatedbycylinder sets.
In the context of a Banach space the cylindrical σ-algebra is defined to be the coarsest σ-algebra (that is, the one with the fewest measurable sets) such that every continuous linear functionon is a measurable function. In general, isnot the same as the Borel σ-algebraon which is the coarsest σ-algebra that contains all open subsets of
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