Related papers: Generalization of the Borel-Cantelli Lemma
In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.
In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.
In this short note, we discuss the Barndorff-Nielsen lemma, which is a generalization of well-known Borel-Cantelli lemma. Although the result stated in the Barndorff-Nielsen lemma is correct, it does not follow from the argument proposed in…
We discuss some conditional generalized Borel-Cantelli lemmas and investigate their quantitative versions following the ideas of Arthan and Oliva (arXiv: 2012.09942).
We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli lemma for systems with sufficiently fast decay of…
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…
Multiple Borel-Cantelli Lemma is a criterion that characterizes the occurrence of multiple rare events on the same time scale. We generalize the multiple Borel-Cantelli Lemma in dynamics established by Dolgopyat, Fayad and Liu [J. Mod. Dyn.…
One of the variants to proof the generalized Ito-Wentzell's formula is introduced and examined in this paper. The relationship between different representations of the generalized Ito-Wentzell's formula/ is considered.
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
In the present paper, a generalization of the first part of the Borel-Cantelli lemma is obtained by the recent work of Balakrishnan and Stepanov (2010). This generalization is further applied to derive strong limit results for the sequence…
In this paper, we propose a generalization of a congruence due to Carlitz.
This paper has been withdrawn by the author due to an error.
In this paper we generalize the approximation theorem for L^2-Betti numbers to an approximation theorem for center-valued Betti-numbers.
We generalise the Bernoulli numbers to include the case where the index may be a continuous variable.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
In this paper we give a quantitative version of the Blow-up Lemma.
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…