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In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field) on a set X is a nonempty collection Σ of subsets of X...

lattice theory Join (topology), an operation combining two topological spaces Join (sigma algebra), a refinement of sigma algebras Join (algebraic geometry)...

In database theory, relational algebra is a theory that uses algebraic structures for modeling data, and defining queries on it with well founded semantics...

mathematics, particularly measure theory, a 𝜎-ideal, or sigma ideal, of a σ-algebra (𝜎, read "sigma") is a subset with certain desirable closure properties...

sets – Algebraic concept in measure theory, also referred to as an algebra of sets Join (sigma algebra) – Algebraic structure of set algebraPages displaying...

algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is...

with the discrete sigma-algebra, and a right adjoint I : Set → Meas which equips a given set with the indiscrete or trivial sigma-algebra. Both of these...

Lie algebras, and various other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and...

complements Set function – Function from sets to numbers σ-algebra – Algebraic structure of set algebra Sigma-ideal – Family closed under subsets and countable...

+ 42 {\displaystyle \sigma (42)=96=3\times 4\times 8=\sigma (2)\times \sigma (3)\times \sigma (7)=1+2+3+6+7+14+21+42} ). Both of these functions are...

Effect algebras are partial algebras which abstract the (partial) algebraic properties of events that can be observed in quantum mechanics. Structures...

Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is...

between Boolean algebras and complete Boolean algebras is the notion of a sigma-algebra. This is defined analogously to complete Boolean algebras, but with...

\varnothing \}} Here, the symbol ∨ {\displaystyle \vee } is the join of sigma algebras, while ∩ {\displaystyle \cap } is set intersection. The equality...

In mathematics, the term homology, originally developed in algebraic topology, has three primary, closely-related usages. The most direct usage of the...

In abstract algebra, a semiring is an algebraic structure. It is a generalization of a ring, dropping the requirement that each element must have an additive...

key characteristic of the modern definitions of both Boolean algebra and sigma-algebra is that they have complement operations. Fraleigh 1976, pp. 25...

several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding...

\scriptstyle v_{0},\ v_{0}+e_{\sigma (1)},\ v_{0}+e_{\sigma (1)}+e_{\sigma (2)}\ldots v_{0}+e_{\sigma (1)}+\cdots +e_{\sigma (n)}} is the set of points v...

σ 2 , σ 3 {\displaystyle \sigma _{1},\sigma _{2},\sigma _{3}} ; these are 2x2 complex matrices that have the Lie algebra property that σ 1 σ 2 − σ 2...