Related papers: A Theorem of Probability

It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.

We present in this work a new and simple proof of the false centre theorem.

We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

To determine whether a number is congruent or not is an old and difficult topic and progress is slow. The paper presents a new theorem when a prime number is a congruent number or not. The proof is not necessarily any simpler or shorter…

We prove that every set $A\subset\mathbb{Z}/p\mathbb{Z}$ with $\mathbb{E}_x\min(1_A*1_A(x),t)\le(2+\delta)t\mathbb{E}_x 1_A(a)$ is very close to an arithmetic progression. Here $p$ stands for a large prime and $\delta,t$ are small real…

An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.

We proove a Bloch's theorem in an almost complex projective plane.

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.

A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives…

A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.

We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.

This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].

We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

The paper gives a unified and simple proof of both theorems and Cousin's theorem.