(mathematics) An important structural theorem in the theory of Banach spaces, essentially stating that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean.

(statistics) A theorem relating to the distribution of the likelihood ratio.

A theorem stating that two connected graphs are isomorphic if and only if their line graphs are isomorphic, with a single exception: K₃, the complete graph on three vertices, and the complete bipartite graph K_(1,3), which are not isomorphic but both have K₃ as their line graph.

A theorem dealing with the relative probability that the entropy of a system that is currently away from thermodynamic equilibrium (i.e. maximum entropy) will increase or decrease over a given amount of time.

(graph theory) A theorem stating that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree.

(graph theory) A theorem that considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.

(mathematics) A theorem in complex analysis concerning the existence of meromorphic functions with prescribed poles.

(set theory) A theorem which (in a simpler formulation) states that a closed uncountable set in Euclidean n-space is equal to the disjoint union of a perfect set and a countable set.

(statistics and mathematics, singular only) The theorem that states that if the sum of independent identically distributed random variables has a finite variance, then it will be approximately normally distributed.

(calculus) A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.