Books in Real functions

Regression Analysis

2nd Edition
March 27, 2006
Rudolf J. Freund + 2 more
English
Hardback
9 7 8 0 1 2 0 8 8 5 9 7 8
eBook
9 7 8 0 0 8 0 5 2 2 9 7 5

Regression Analysis provides complete coverage of the classical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design.

Mathematical Inequalities

1st Edition
Volume 67
May 4, 2005
B. G. Pachpatte
English
eBook
9 7 8 0 0 8 0 4 5 9 3 9 4

The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics.

Theories of Generalised Functions

1st Edition
January 1, 2005
R F Hoskins + 1 more
English
Paperback
9 7 8 1 8 9 8 5 6 3 9 8 3
eBook
9 7 8 0 8 5 7 0 9 9 4 8 8

Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins.

Nonmeasurable Sets and Functions

1st Edition
Volume 195
May 29, 2004
Alexander Kharazishvili
English
eBook
9 7 8 0 0 8 0 4 7 9 7 6 7

The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-measurable cardinals;3. The theory of invariant (quasi-invariant)extensions of invariant (quasi-invariant) measures.These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.

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Books in Real functions

Regression Analysis

Mathematical Inequalities

Theories of Generalised Functions

Nonmeasurable Sets and Functions