A Short Proof of the Birkhoff-von Neumann Theorem

An Algorithmic Proof of a Generalization of the Birkhoff-Von Neumann Theorem

Mathema Tics: E. Hille

from which, dividing through by N, and letting N -a, we will get X(h) . a(h) en(h) e. Now letting e -O 0, the proof is complete. The proof of (E) reproduces the combinatorial essence of G. D. Birkhoff's proof of the Strong Ergodic Theorem.2 We rely on the fact that the "components" of h form a Boolean algebra, and may be treated like sets. 1 L. Kantorovitch. "Lineare halbgeordnete Raume," Math....

On New Forms of the Ergodic Theorem

We present generalizations of the classical Birkhoff and von Neumann ergodic theorems, where the time average is replaced by a more general average, including some density.

Minimum Birkhoff-von Neumann Decomposition

Motivated by the applications in routing in data centers, we study the problem of expressing an n × n doubly stochastic matrix as a linear combination using the smallest number of (sub)permutation matrices. The Birkhoff-von Neumann decomposition theorem proves that there exists such a decomposition, but does not give a representation with the smallest number of permutation matrices. In particul...

A SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS

In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.