Re: Sikorski - Funkcje rzeczywiste I

From: Dave L. Renfro (renfr1dl_at_cmich.edu)
Date: 02/28/05 

Date: Mon, 28 Feb 2005 19:45:10 +0000 (UTC)

Dave L. Renfro <renfr1dl@cmich.edu>
[sci.math: February 28, 2005 11:58:05:000AM]
http://mathforum.org/discuss/sci.math/m/688089/688139

Martin wrote (in part)

>> Or maybe you could have another good hint for a book about
>> real functions. Some topics that I'm interested in are:
>> Borel categories of sets, Baire classes of sets, their
>> relationship, Baire classes of sets and composition,
>> limits, limsup... and many others one could call
>> "classical" but I haven't found a good and detailed
>> resource about them so far.

Dave L. Renfro wrote:

[snip references I provided]

Oh, I just noticed that you were asking about classical
real function theory in general, and not just about Borel
sets and Baire functions. Regarding this more general
topic, I'd recommend the following (Boas, Buckner/Thomson,
Goffman, Hahn, Oxtoby, and Rooij/Schikhof the most):

          ------------------------------------

John J. Benedetto, REAL VARIABLE AND INTEGRATION,
Mathematische Leitfäden. Stuttgart: B. G. Teubne, 1976.

Ralph P. Boas, A PRIMER OF REAL FUNCTIONS, 4'th edition
(revised and updated by Harold P. Boas), Carus Mathematical
Monographs 13R, The Mathematical Association of America, 1996.

Andrew M. Bruckner, Judith B. Bruckner, and Brian S. Thomson,
REAL ANALYSIS, Prentice-Hall, 1997.

James Foran, FUNDAMENTALS OF REAL ANALYSIS, Pure and Applied
Mathematics #144, Marcel Dekker, 1991.

Casper Goffman, REAL FUNCTIONS, Prindle, Weber & Schmidt, 1953.

Hans Hahn, REELLE FUNKTIONEN, Akademie Verlagsgesellschaft,
Leipzig, 1932. [Reprinted by Chelsea in 1948.]

Ernest W. Hobson, THE THEORY OF FUNCTIONS OF A REAL VARIABLE
AND THE THEORY OF FOURIER'S SERIES, VolumeS I & II, Dover
Publications, 1927/1957 & 1926/1957.

Wieslawa J. Kaczor and Maria T. Nowak, PROBLEMS IN MATHEMATICAL
ANALYSIS II: CONTINUITY AND DIFFERENTIATION, Student
Mathematical Library #12, American Mathematical Society, 2001.

Rangachary Kannan and Carole King Krueger, ADVANCED ANALYSIS
ON THE REAL LINE, Springer-Verlag, 1996.

Miklós Mikolás, REAL FUNCTIONS, ABSTRACT SPACES AND
ORTHOGONAL SERIES, Akadémiai Kiadó (Publishing House
of the Hungarian Academy of Sciences), 1994.

John C. Oxtoby, MEASURE AND CATEGORY, 2'nd edition,
Graduate Texts in Mathematics #2, Springer-Verlag, 1980.

Arnoud C. M. Van Rooij and Wilhelmus H. Schikhof, A SECOND
COURSE ON REAL FUNCTIONS, Cambridge University Press, 1982.

Edgar Jerome Townsend, FUNCTIONS OF REAL VARIABLES,
Henry Holt and Company, 1928.

          ------------------------------------

Dave L. Renfro