Related papers: On Egorov's Theorem for Infinite Measure

In this paper, we prove a structure theorem for the infinite union of $n$-adic doubling measures via techniques which involve far numbers. Our approach extends the results of Wu in 1998, and as a by product, we also prove a classification…

In this article, we prove a limit theorem for an observable on the torus with a singularity of type $x^{-a}$, where $0<a<1$.

The third part of the paper concludes the proof of the main result --- the description of the ergodic decomposition of infinite Pickrell measures. First it is shown that the scaling limit of radial parts of finite-dimensional infinite…

We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…

In this note, we give a simple proof that the values of the trigonometric functions at any nonzero rational number are transcendental numbers.

In this note we give a detailed proof of a theorem of Aubin.

We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.

In this paper we present a short and elementary proof for the error in Simpson's rule.

This is a note of purely didactical purpose as the proof of the Jordan measure decomposition is often omitted in the related literature. Elementary proofs are provided for the existence, the uniqueness, and the minimality property of the…

Erd\H{o}s-Ginzburg-Ziv theorem says that if there are 2n-1 number is given, then there are n numbers such that their sum is divided by n. We will connect this theorem with the Ramsey theoretic large sets and will prove an infinitary version…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all…

The goal of this paper is to give a detailed and complete proof of M. Gromov's waist of the sphere theorem.

This paper aims to give an elementary proof for Toponogov's theorem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian geometry, sectional curvature can be embodied in the second…

We prove a $C^\infty$ version of the Nekhoroshev's estimate on the stability times of the actions in close to integrable Hamiltonian systems. The proof we give is a variant of the original Nekhoroshev's proof and it consists in first…

We prove several results concerning the discrepancy, tested on balls in the $d$-dimensional torus $\mathbb{T}^{d}$, between absolutely continuous measures and finite atomic measures.

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.