Birkhoff's theorem may refer to several theorems named for the American mathematician
George David Birkhoff
George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and duri ...
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Birkhoff's theorem (relativity)
In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution (i.e. the spacetime outside of a spherical, n ...
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Birkhoff's theorem (electromagnetism) In physics, in the context of electromagnetism, Birkhoff's theorem concerns spherically symmetric static solutions of Maxwell's field equations of electromagnetism.
The theorem is due to George D. Birkhoff. It states that any spherically symmetric ...
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Birkhoff's ergodic theorem
Ergodic theory ( Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are exp ...
It may also refer to theorems named for his son,
Garrett Birkhoff
Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician. He is best known for his work in lattice theory.
The mathematician George Birkhoff (1884–1944) was his father.
Life
The son of the mathematician G ...
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Birkhoff–von Neumann theorem for doubly stochastic matrices
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Birkhoff's HSP theorem
In universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of identities. For example, the groups form a variety of algebras, as do the abelian groups, th ...
, concerning the closure operations of homomorphism, subalgebra and product
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Birkhoff's representation theorem
:''This is about lattice theory. For other similarly named results, see Birkhoff's theorem (disambiguation).''
In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive latti ...
for distributive lattices
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Birkhoff's theorem (equational logic)
In logic, Birkhoff's theorem in equational logic states that an equality t = u is a semantic consequence of a set of equalities
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expression ...
, stating that syntactic and semantic consequence coincide
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