Algebra Generated

Some articles on algebras, generated:

Statistical Dependence - Definition - Independent σ-algebras
... both generalized by the following definition of independence for σ-algebras ... Let (Ω, Σ, Pr) be a probability space and let A and B be two sub-σ-algebras of Σ ... A ∈ A and B ∈ B, Likewise, a finite family of σ-algebras is said to be independent if and only if for all and an infinite family of σ-algebras is said to ...
Invariant Theory - Hilbert's Theorems
... the ring of polynomials R = S(V) is finitely generated ... so is graded by degrees, and the ideal I is defined to be the ideal generated by the homogeneous invariants of positive degrees ... By Hilbert's basis theorem the ideal I is finitely generated (as an ideal) ...

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