Related papers: Hoeffding's inequality in game-theoretic probabili…
We prove game-theoretic generalizations of some well known zero-one laws. Our proofs make the martingales behind the laws explicit, and our results illustrate how martingale arguments can have implications going beyond measure-theoretic…
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
We prove some extensions of Andrews inequality.
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…
The Parrondo's paradox is a counterintuitive phenomenon where individually-losing strategies can be combined in producing a winning expectation. In this paper, the issues surrounding the Parrondo's paradox are investigated. The focus is…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Equivalencies of many basic elementary inequalities are given
We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some…
For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…
On being told that a piece of work he thought was his discovery had duplicated an earlier mathematician's work, Larry Shepp once replied "Yes, but when {\em I} discovered it, it {\em stayed} discovered". In this spirit we give discussion…
In this note by using elementary considerations, we settle Fr\"oberg's conjecture for a large number of cases, when all generators of ideals have the same degree.
In literature the Hermite-Hadamard inequality was eligible for many reasons, one of the most surprising and interesting that the Hermite-Hadamard inequality combine the midpoint and trapezoid formulae in an inequality. In this work, a…
The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…
Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…
The status and regime of validity of the famous Thorne hoop conjecture in spatially regular {\it charged} curved spacetimes are clarified.