Related papers: On Egorov's Theorem for Infinite Measure

The aim of this paper is to prove ergodic decomposition theorems for probability measures quasi-invariant under Borel actions of inductively compact groups (Theorem 1) as well as for sigma-finite invariant measures (Corollary 1). For…

In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We extend almost everywhere convergence in Wiener-Wintner ergodic theorem for $\sigma$-finite measure to a generally stronger almost uniform convergence and present a larger, universal, space for which this convergence holds. We then extend…

We provide a direct proof of Agafonov's theorem which states that finite state selection preserves normality. We also extends this result to the more general setting of shifts of finite type by defining selections which are compatible the…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.

A short proof is given for the well-known Choi-Effros theorem on the structure of ranges of completely positive projections.

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.

We show that ``ergodic regime'' appears for generic dispersion relations in the semiclassical motion of electrons in a metal and we prove that, in the fixed energy picture, the measure of the set of such directions is zero.

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

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

A one-line proof of a minimax theorem due to Steinerberger is given.

This is just a short proof of Kruskal's theorem regarding uniqueness of expressions for tensors, phrased in geometric language.

We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.

We give a proof of an infinitary version of the well known Hales-Jewett theorem on finite words avoiding the use of ultrafilters.

Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.