A simple proof for Schur's theorem

In 1917 Schur gave a characterization of bounded analytic functions on the unit disc. We present a simple proof.

     

A simple proof for the matrix-geometric theorem

For block-partitioned matrices of the GI/M/1 type, it has been shown by M. F. Neuts that the stationary probability vector, when it exists, has a matrix-geometric form. We present here a new proof, which we believe to be the simplest available today.     

A simple proof for the Chernoff-Savage theorem

A proof for the Chernoff-Savage theorem is given based on differentiable statistical functionals. It employs no second order differentiability condition.     

A proof of Shelah's partition theorem

A self contained proof of Shelah's theorem is presented: If is a strong limit singular cardinal of uncountable cofinality and 2 > ⁺ then .     

A new proof of Poltoratskii's theorem

We provide a new simple proof to the celebrated theorem of Poltoratskii concerning ratios of Borel transforms of measures. That is, we show that for any complex Borel measure μ on and any a.e. w.r.t. μ_sing, where μ_sing is the part of μ which is singular with respect to Lebesgue measure and F denotes a Borel transform, namely, and F_μ(z)=∫(x−z)⁻¹dμ(x).     

A short proof of Fan's theorem

In this note, we give a new short proof of the following theorem: Let G be a 2-connected graph of order n. If for any two vertices u and v with d(u,v)=2,max{d(u),d(v)}?c/2, then the circumference of G is at least c, where 3?c?n and d(u,v) is the distance between u and v in G.     

A proof of the Dvoretzky-Rogers theorem

We give a new proof of the famous Dvoretzky-Rogers theorem ([2], Theorem 1), according to which a Banach spaceE is finite-dimensional if every unconditionally convergent series inE is absolutely convergent.     

A new proof of Mayer''s theorem

This paper gives a new proof of Mayer's theorem concerning the convergence of powers of an interval matrix.     

A variational proof of Aumann's theorem

We give a new proof of Aumann's theorem on the integrals of multifunctions. The proof, which is variational in nature, also leads to a constructive procedure for calculating a selection whose integral approximates a given point in the integral of the multifunction.The support of the Natural Sciences and Engineering Research Council of Canada (grant A 9082) and of the Killam Foundation (Canada Council Senior Research Fellowship) is gratefully acknowledged.