Related papers: Generalization of the Borel-Cantelli Lemma

A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

A generalization of the law of total covariance is presented and proved.

The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.

We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

The Riccati equation method is used to obtain a generalization of the Gronvall-Bellman lemma the obtained result is used to generalize a result of Lyapunov.

We analyze a system of linear algebraic equations whose solutions lead to a proof of a generalization of Boole's formula. In particular, our approach provides an elementary and short alternative to Katsuura's proof of this generalization.

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We generalize Bulitko's Lemma to equations over (or homomorphisms into) groups that have $\kappa$-acylindrical splittings.

We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

We prove some new results related to Tanaka's formula.

In this note we give an extended version of Combinatorial Nullstellensatz, with weaker assumption on nonvanishing monomial. We also present an application of our result in a situation where the original theorem does not seem to work.

In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.

In this article we discuss a generalized Wirtinger inequality.

Let $\{A_n\}_{n=1}^\infty$ be a sequence of events and let $\displaystyle S:=\sum_{n=1}^\infty 1_{A_n}$. We present in this note equivalent characterizations for the statements $\mathbb{P} (S<\infty)=1$ and $\mathbb{P} (S=\infty)=1$…

In this paper we propose and solve a generalization of the Bernoulli Differential Equation, by means of a generalized fractional derivative. First we prove a generalization of Gronwall's inequality, which is useful for studying the…

In this note a generalization of the Lamb-Bateman integral equation is presented and its solution is given in terms of {\bf fractional derivatives}. This is a comment one to the paper by Babusci, Dattoli and Sacchetti (arXiv:1006.0184…

The purpose of this note is to show by constructing counterexamples that two conjectures of M\'{o}ri and Sz\'{e}kely for the Borel-Cantelli lemma are false.