Related papers: A Theorem of Probability

We obtain an almost sure limit theorem for the maximum of nonstationary random fields under some dependence conditions.

This article establishes a real-variable argument for Zygmund's theorem on almost everywhere convergence of strong arithmetic means of partial sums of Fourier series on $\mathbb{T}$, up to passing to a subsequence. Our approach extends to,…

We prove an effective version of the Oppenheim conjecture with a polynomial error rate. The proof is based on an effective equidistribution theorem which in turn relies on recent progress towards restricted projection problem.

This is an introduction to some of the most probabilistic aspects of free probability theory.

A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…

We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.

We prove a uniformization theorem in complex algebraic geometry.

An equivalent but useful version on the Homological Nerve Theorem is proved.

General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is…

I provide simplified proofs for each of the following fundamental theorems regarding selection principles: 1. The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of…

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

We prove that every transitive and non minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result.

We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

Consider a walk in the plane made of $n$ unit steps, with directions chosen independently and uniformly at random at each step. Rayleigh's theorem asserts that the probability for such a walk to end at a distance less than 1 from its…

Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.

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