Related papers: On Egorov's Theorem for Infinite Measure

We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measures are well-known and have been used in the literature to prove Poncelet's and Zigzag theorems. Some…

We present an elementary proof for Ljunggren equation

We provide a simple proof of Kamp's theorem.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

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 result generalises the ones given up to date.

In this paper, we review the basic properties of measures vanishing at infinity and prove a version of the Riemann--Lebesgue lemma for Fourier transformable measures.

In this paper we review a general proof for the irrationality property of numbers which take a certain form of infinite sums.

We deduce the existence of a maximal irreducibility measure for a Markov chain from Zorn's lemma.

We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.

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

In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.

I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.

The Egoroff theorem for measurable $\bold X$-valued functions and operator-valued measures $\bold m: \Sigma \to L(\bold X, \bold Y)$, where $\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and $\bold X$, $\bold Y$ are both…

We provide new simple proofs of the Kolmogorov extension theorem and Prokhorovs' theorem. The proof of the Kolmogorov extension theorem is based on the simple observation that $\mathbb{R}$ and the product measurable space…

Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.

A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.

A simple proof of the weighted two variable geometric-arithmetic a mean inequality based on one given earlier valid only for integer weights