eBook ISBN:  9780821876275 
Product Code:  CONM/42.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876275 
Product Code:  CONM/42.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 42; 1985; 216 ppMSC: Primary 00; Secondary 28
This book collects most of the papers presented at a special session on classical real analysis held to honor Casper Goffman at the April 1982 AMS meeting. The variety of these papers reflects Goffman's wideranging interests and the many areas where his influence has been felt: differentiation and integration theory, structure theory of real functions, ordered systems, surface area, Sobolev spaces, Fourier analysis, measure theory, bases, and approximation theory. Together they provide an appreciation of the directions in which real analysis has developed and of how classical techniques might be applied to problems of current interest.
Readers should have a background in classical analysis. Though aimed primarily at specialists in real function theory of one or several variables, the papers will also interest mathematicians working in the areas of Fourier analysis, surface area, mapping theory and control theory.

Table of Contents

Articles

Casper Goffman — Cesari spaces and Sobolev spaces in surface area and localization for multiple Fourier series [ MR 807971 ]

B. Bongiorno and D. Preiss — An unusual descriptive definition of integral [ MR 807972 ]

A. M. Bruckner, R. J. O’Malley and B. S. Thomson — Path derivatives: a unified view of certain generalized derivatives [ MR 807973 ]

A. M. Bruckner, J. Mařík and C. E. Weil — Baire one, null functions [ MR 807974 ]

Richard Darst and Robert Huotari — Monotone approximation on an interval [ MR 807975 ]

Roy O. Davies — Two remarks on the measure of product sets [ MR 807976 ]

Michael J. Evans and Lee Larson — Monotonicity, symmetry, and smoothness [ MR 807977 ]

James Foran — The structure of continuous functions which satisfy Lusin’s condition $({\rm N})$ [ MR 807978 ]

K. M. Garg — Construction of absolutely continuous and singular functions that are nowhere of monotonic type [ MR 807979 ]

P. D. Humke and B. S. Thomson — A porosity characterization of symmetric perfect sets [ MR 807980 ]

Lee Larson — A method for showing generalized derivatives are in Baire class one [ MR 807981 ]

Cheng Ming Lee — On generalizations of exact Peano derivatives [ MR 807982 ]

David Legg — Best monotone approximation in $L_\infty [0,1]$ [ MR 807983 ]

Fon Che Liu — Representation of lattices and extension of measures [ MR 807984 ]

Jan Mařík — Transformation and multiplication of derivatives [ MR 807985 ]

J. H. Michael and William P. Ziemer — A Lusin type approximation of Sobolev functions by smooth functions [ MR 807986 ]

C. J. Neugebauer — Some properties of Fourier series with gaps [ MR 807987 ]

Togo Nishiura — An extension of Thunsdorff’s integral inequality to a class of monotone functions [ MR 807988 ]

L. Di Piazza and C. Maniscalco — On generalized bounded variation [ MR 807989 ]

B. S. Thomson — On the level set structure of a continuous function [ MR 807990 ]

Si Lei Wang — Some properties of the LittlewoodPaley $g$function [ MR 807991 ]

Daniel Waterman — Changeofvariable invariant classes of functions and convergence of Fourier series [ MR 807992 ]

Robert E. Zink — Schauder bases for $L^p[0,1]$ derived from subsystems of the Schauder system [ MR 807993 ]


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
This book collects most of the papers presented at a special session on classical real analysis held to honor Casper Goffman at the April 1982 AMS meeting. The variety of these papers reflects Goffman's wideranging interests and the many areas where his influence has been felt: differentiation and integration theory, structure theory of real functions, ordered systems, surface area, Sobolev spaces, Fourier analysis, measure theory, bases, and approximation theory. Together they provide an appreciation of the directions in which real analysis has developed and of how classical techniques might be applied to problems of current interest.
Readers should have a background in classical analysis. Though aimed primarily at specialists in real function theory of one or several variables, the papers will also interest mathematicians working in the areas of Fourier analysis, surface area, mapping theory and control theory.

Articles

Casper Goffman — Cesari spaces and Sobolev spaces in surface area and localization for multiple Fourier series [ MR 807971 ]

B. Bongiorno and D. Preiss — An unusual descriptive definition of integral [ MR 807972 ]

A. M. Bruckner, R. J. O’Malley and B. S. Thomson — Path derivatives: a unified view of certain generalized derivatives [ MR 807973 ]

A. M. Bruckner, J. Mařík and C. E. Weil — Baire one, null functions [ MR 807974 ]

Richard Darst and Robert Huotari — Monotone approximation on an interval [ MR 807975 ]

Roy O. Davies — Two remarks on the measure of product sets [ MR 807976 ]

Michael J. Evans and Lee Larson — Monotonicity, symmetry, and smoothness [ MR 807977 ]

James Foran — The structure of continuous functions which satisfy Lusin’s condition $({\rm N})$ [ MR 807978 ]

K. M. Garg — Construction of absolutely continuous and singular functions that are nowhere of monotonic type [ MR 807979 ]

P. D. Humke and B. S. Thomson — A porosity characterization of symmetric perfect sets [ MR 807980 ]

Lee Larson — A method for showing generalized derivatives are in Baire class one [ MR 807981 ]

Cheng Ming Lee — On generalizations of exact Peano derivatives [ MR 807982 ]

David Legg — Best monotone approximation in $L_\infty [0,1]$ [ MR 807983 ]

Fon Che Liu — Representation of lattices and extension of measures [ MR 807984 ]

Jan Mařík — Transformation and multiplication of derivatives [ MR 807985 ]

J. H. Michael and William P. Ziemer — A Lusin type approximation of Sobolev functions by smooth functions [ MR 807986 ]

C. J. Neugebauer — Some properties of Fourier series with gaps [ MR 807987 ]

Togo Nishiura — An extension of Thunsdorff’s integral inequality to a class of monotone functions [ MR 807988 ]

L. Di Piazza and C. Maniscalco — On generalized bounded variation [ MR 807989 ]

B. S. Thomson — On the level set structure of a continuous function [ MR 807990 ]

Si Lei Wang — Some properties of the LittlewoodPaley $g$function [ MR 807991 ]

Daniel Waterman — Changeofvariable invariant classes of functions and convergence of Fourier series [ MR 807992 ]

Robert E. Zink — Schauder bases for $L^p[0,1]$ derived from subsystems of the Schauder system [ MR 807993 ]