Related papers: Chernoff's Inequality - A very elementary proof

We prove several extensions of the Erdos-Fuchs theorem.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics…

We provide a simple proof of Kamp's theorem.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

We prove a stability version of the Pr\'ekopa-Leindler inequality.

I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

We provide an alternating proof of sharp inequalities related with Burnside's formula for $n!$

In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the population of an arbitrary random vector X…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

The classical Chernoff's theorem is a statement about discrete-time approximations of semigroups, where the approximations are consturcted as products of time-dependent contraction operators strongly differentiable at zero. We generalize…

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

Vapnik--Chervonenkis' theorem is a seminal result in machine learning. It establishes sufficient conditions for empirical probabilities to converge to theoretical probabilities, uniformly over families of events. It also provides an…

In this paper,we will give an easy example to satisfy that we can not conclude CDE' Inequality just from the CD Inequality.

We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the…

Using nonstandard analysis, an intuitive and very short proof of the Radon-Nikodym theorem is provided