This book offers a clear and comprehensive introduction to the Lebesgue integral — one of the foundational concepts of modern analysis. Beginning with the historical development of integration, it ...

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

ABSTRACT: In this paper, by applying the extension of Rubio de Francia’s extrapolation theorem in Lebesgue spaces with variable exponent, the boundedness of the θ-type Calderón-Zygmund operator T θ is ...

Daniel Liberto is a journalist with over 10 years of experience working with publications such as the Financial Times, The Independent, and Investors Chronicle. Eric's career includes extensive work ...

Abstract: We formulate the Lebesgue-sampling-based optimal control problem. We show that the problem can be solved by the time aggregation approach in Markov decision processes (MDP) theory.

Whether or not you’ve heard the term “queer theory,” it’s likely to have impacted some aspect of your life. Click through to learn what queer theory is, how it's used, and who has been involved with ...

For length and area, a central fact is that the value of the length of a curve or the area of a surface, as given by the Lebesgue theory, is at least as great as that given by the classical formula, ...

THE author of this book complains that while Lebesgue integration is everywhere firmly established as an essential part of the theory of functions, its treatment in English text-books “remains ...

The author is a Sloan Foundation Fellow. During part of the period when this paper was prepared, he received support from NSF contract GP-8746.

Whether a child is the firstborn, a middle child, the youngest, or an only child may affect how their family treats them, how much attention they receive, and how they may compete for their parents’ ...

In the past few years, I’ve moved more than once. Time and again, I have had to measure rooms or furniture and then check whether I can arrange everything just as I had planned. When we use a tape ...