Unfortunately, though the Kolmogorov Arnold representation theorem asserts the existence of a function of this form, it gives no mechanism whereby one could be constructed.
42.
More formally, the Riesz representation theorem implies that for all x in X there exists a unique element K _ x of H with the reproducing property,
43.
The " universal " property has important applications in functional analysis, where it is sometimes known as the " representation theorem for compact metric spaces ".
44.
Birkhoff's representation theorem for distributive lattices states that every " finite " distributive lattice is isomorphic to the lattice of monotone functions of finite posets.
45.
Another early representation theorem is now known as Stone's representation theorem for distributive lattices ( the name honors Marshall Harvey Stone, who first proved it ).
46.
Another early representation theorem is now known as Stone's representation theorem for distributive lattices ( the name honors Marshall Harvey Stone, who first proved it ).
47.
One of the most useful results from Malliavin calculus is the Clark-Ocone theorem, which allows the process in the martingale representation theorem to be identified explicitly.
48.
It had been known since the 1950s ( via . the Kolmogorov Arnold representation theorem ) that any multivariate function could be represented as sums and compositions of univariate functions.
49.
In mathematics, the "'Riesz Markov Kakutani representation theorem "'relates linear functionals on spaces of continuous functions on a locally compact space to measures.
50.
It is the basis of Stone's representation theorem for Boolean algebras and an example of a completion procedure in order theory based on filters, similar to Dedekind cuts.
