Related papers: The choosability version of Brooks' theorem -- a s…

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

We expose here a short proof of Cramer's theorem in R based on convex duality.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

The article considers the Choice Axiom.

We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

We prove several extensions of the Erdos-Fuchs theorem.

In this note, we will give a short proof of an identity for cubic partitions.

We proove a Bloch's theorem in an almost complex projective plane.

A proof is given of Rosenthal's \(\ell_1\) theorem.

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

We prove an infinitary version of the Brauer-Schur theorem.

A very simple but useful almost sure convergence theorem of probability is given.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

We provide a simple proof of Kamp's theorem.

We produce a new, shorter construction of a minor-universal planar graph.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.