Provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesg…
This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics…
Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to …
by Brokate, Martin, Kersting, Götz
fromCompact textbooks in mathematics
The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of t…
by Brokate, Martin, Kersting, Götz
fromCompact textbooks in mathematics
by Brokate, Martin, Kersting, Götz
fromCompact textbooks in mathematics
"Measure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory …
This classroom-tested text is intended for a one-semester course in Lebesgue's theory. With over 180 exercises, the texttakes an elementary approach, making iteasily accessible toboth upper-undergraduate- and lower-graduate-level students. The three main topics presented are mea…
