Related papers: On Egorov's Theorem for Infinite Measure

We consider the generalized Egorov's statement (Egorov's Theorem without the assumption on measurability of the functions, see \cite{tw:nget}) in the case of an ideal convergence and a number of different types of ideal convergence notion.…

In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

A proof of Sendov's conjecture is given.

We prove a model theorem for factor maps between ergodic, infinite measure-preserving systems.

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

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

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

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

We give a purely combinatorial proof for the infinitary van der Waerden's theorem.

In this paper a free analogous of completely random measure is introduced. Furthermore, a representation theorem is proved for free completely random measures that are free infinitely divisible.

We prove existence of an invariant measure on a hypergroup.

We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.

In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.

We present a simple inductive proof of the Lagrange Inversion Formula.

We prove an analogue of the prime number theorem for finite fields.

We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…