Related papers: A variation of Gronwall's lemma

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

An technically interesting proof of a known theorem.

We prove the Aharoni Berger Conjecture

We prove a local version of the Mazur-Ulam theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

We prove existence of an invariant measure on a hypergroup.

In the present note a generalization of Borel-Cantelli Lemma is proposed.

We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.

In this note we prove a weighted version of the Khintchine inequalities.

A proof is given of Rosenthal's \(\ell_1\) theorem.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

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

We prove several extensions of the Erdos-Fuchs theorem.

In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.

We prove some extensions of Andrews inequality.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

In this paper we prove the WALA conjecture.

We prove the following version generalization of the Gronwall inequality: Let $\mathbf X$ be a Banach space and $U\subset \mathbf X$ an open convex set in $\mathbf X$. Let $f,g\colon [a,b]\times U\to \mathbf X$ be continuous functions and…