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

The purpose of the paper is to present an short proof of the Chuang's inequality.

We prove an easy but very weak version of Chernoff inequality. Namely, that the probability that in $6M$ throws of a fair coin, one gets at most $M$ heads is $\leq 1/2^M$.

We present simple randomized and exchangeable improvements of Markov's inequality, as well as Chebyshev's inequality and Chernoff bounds. Our variants are never worse and typically strictly more powerful than the original inequalities. The…

We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

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

We discuss five ways of proving Chernoff's bound and show how they lead to different extensions of the basic bound.

We prove some extensions of Andrews inequality.

In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.

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

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

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

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We present a relative form of the Toponogov comparison theorem.

We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.

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.

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 simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…