Derivates of interval functions / Brian S. Thomson.

Format:

Book

Author/Creator:

Thomson, Brian S., 1941- author.

Contributor:

American Mathematical Society.

Series:

Memoirs of the American Mathematical Society ; Volume 93, Number 452.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 93, Number 452

Language:

English

Subjects (All):

Interval functions.

Differentiable functions.

Physical Description:

1 online resource (106 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1991.

Language Note:

English

Summary:

In the study of the derivation properties of interval functions, there are certain arguments that reappear in many settings. In this book, the author seeks to present a unified approach to some of these techniques. The motivation grows out of the interesting and important study of Rogers and Taylor characterizing those interval functions which are, in a sense, absolutely continuous with respect to the 8-dimensional Hausdorff measure. This problem leads naturally to an investigation of Lipschitz numbers Ds(f,x) = lim sup y,z ?x,y

Contents:

""Contents""; ""1 Introduction""; ""2 Covering relations""; ""2.1 Basic language of covering relations""; ""2.2 Full and fine covering""; ""2.3 Covering lemmas""; ""3 The variation""; ""3.1 Variation of an interval�point function""; ""3.2 Differential equivalence""; ""3.3 Variational measures""; ""3.4 Increasing sets property""; ""3.5 Regularity properties""; ""3.6 The upper integral""; ""3.7 The variational measure as an integral""; ""3.8 The fine variational measure as an integral""; ""3.9 Differential equivalence""; ""3.10 A density theorem""; ""4 Derivates""

""4.1 Definitions of the derivates""""4.2 Baire class of derivates""; ""4.3 Variational estimates""; ""4.4 Lipschitz conditions""; ""4.5 Exact derivatives""; ""5 Absolute continuity and singularity""; ""5.1 Basic Definitions""; ""5.2 Further properties""; ""5.3 Measure properties""; ""5.4 A stronger orthogonality relation""; ""5.5 Derivation properties and singularity""; ""5.6 Characterization of singularity""; ""5.7 Derivation properties and absolute continuity""; ""5.8 Characterization of absolute continuity""; ""6 Measures""; ""6.1 Lebesgue measure""; ""6.2 Total variation measures""

Notes:

"September 1991, Volume 93, Number 452 (first of 3 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0878-3