Real Analysis

Updated: October, 1998

Report on the

(The ANDY Symposium)
University of California at Santa Barbara
June 23 -- 27, 1998

The Twenty-Second Summer Symposium in Real Analysis was held at the University of California at Santa Barbara, June 23 -- 27, 1997 and was held to celebrate the contributions Andy Bruckner has made to real analysis. The conference was sponsored by the National Science Foundation (Grant #DMS-9800357), The TRW Corporation, The Faculty Senate of the University of California-Santa Barbara, former recipients of the coveted And, and and Andy's Ph.D. students. Without the generous financial help supplied by these organizations, the scope of the conference would have been significantly narrower. The Editorial Board of the Exchange and the participants of the conference thank them.

The conference was ably organized by Professor Charles Akemann (UC-Santa Barbara), Paul Humke (St. Olaf College) and T.H. Steele (Weber State University) and the Editorial Board of the Exchange wishes to take this opportunity to gratefully acknowledge their leadership in this endeavor.

At the traditional Friday evening banquet various participant's took turns ``roasting'' and warmly honoring Andy Bruckner. At the conclusion of the evening Paul Humke announced that this year's recipient of the ANDY award is appropriately Judy Bruckner. Congratulations, Judy and thank you for sharing Andy with us.

The conference featured invited fifty-minute addresses by:

Casper Goffman, West Lafeyette
Miklos Laczkovich, Budapest
Alexander Olevskii, Tel Aviv
Gyorgy Petruska, Budapest
Brian Thomson, Vancouver
Perti Mattila, Jyvaskyla

as well as thirty-one twenty-minute contributed talks.


Steve Agronsky (San Luis Obispo) Charles Akemann (Santa Barbara)
J. Marshall Ash (Chicago) Harold Atkinson (Windsor)
Bob Biskner (Santa Barbara) George U. Brauer (Minneapolis)
Jack B. Brown ( Auburn) Jane Brown (Auburn)
Andrew M. Bruckner (Santa Barbara) Judith Bruckner (Santa Barbara)
Zolt\'an Buczolich ( Budapest) Peter Bullen (Vancouver)
Alietia Caughron (Kansas City)< Jack Ceder (Santa Barbara)
Krzysztof Ciesielski ( Morgantown) Mark Coodey (Malibu)
Marianna Cs\"{o}nyei (Budapest) Emma D'Aniello (Naples)
Thierry De Pauw (Louvain-la Neuve) Martin Dindos (Chapel Hill)
Hussain Elalaoui-Talibi (Auburn) Michael J. Evans (Lexington)
Henry Fast (San Jose) Hajrudin Fejzic ( San Bernardino)
James Foran ( Kansas City) Chris Freiling (San Bernardino)
Ian June L. Garces (Manila) Krishna M. Garg (Edmonton)
Casper Goffman (West Lafeyette) Russell Gordon (Walla Walla)
Raymond Grinnell (Bridgetown) Don Hancock (Algoura Hills)
Ralph Henstock ( Coleraine) Eric Howard (Kirksville)
Paul D. Humke (Northfield) Sara Jones (Colorado Springs)
Greg Kaestle (Agoura Hills) Judit Kardos (East Windsor)
Tam\'{a}s Keleti (Budapest) Kenneth Kellum (San Jose)
Mikl\'{o}s Laczkovich (Budapest) Cheng-Ming Lee ( Milwaukee)
Larry Lindsay (Denton) Rick Mabry (Shreveport)
Anna B. Maciejewska (Louisville) Pertti Mattila (Jyv\"askyl\"a)
Mark McClure (Asheville) Alica Miller (East Lansing)
Christopher K. Miller (Goleta) Michal Morayne (Wroc\l aw)
John C. Morgan II (Pomona) Shizu Nakanishi (Osaka)
C. J. Neugebauer (West Lafayette) Togo Nishiura (Carlisle)
Richard O'Malley (Milwaukee) Jimmy Peterson (Normal)
Gyorgy Petruska (Budapest) Pamela Pierce (Wooster)
Dave L. Renfro (Natchitoches) Giuseppa Riccobono (Palermo)
Dan Rinne (San Bernardino) Hongjian Shi (Burnaby)
Jaroslav Sm\'{\i}tal (Opava) David Sprecher (Montecito)
T. H. Steele (Ogden) Jason H. Steffen (Fruit Heights)
A. H. Stone (Brookline) Dorothy Maharam Stone ( Brookline)
Ralph Svetic ( Milwaukee) Brian S. Thomson (Burnaby)
Tim Traynor ( Windsor) Robert W. Vallin (Slippery Rock)
Hans Volkmer ( Milwaukee) Jeremy Walthers (Ogden)
Daniel Waterman (Boynton Beach) Jo Ann Weller (Lee's Summit)
Nahum Zobin (Columbus)


TUESDAY Evening:

Special Lecture by Casper Goffman
Some of Andy's Contributions to Real Analysis
Introduction by Richard O'Malley

WEDNESDAY Morning: ( Chairs: Peter Bullen and Zoltan Buczolich )

08:10 Brian ThomsonSome influences
09:10 Russell Gordon The Bounded Convergence Theorem for the Riemann integral
09:40 Giuseppa Riccobono A PU-integral on a compact topological measure space
10:40 John C. MorganII Transcendental point set theory
11:10 Krishna Garg A unified theory of unilateral derivates
11:40 Rick Mabry Subsets of the plane having constant linear shade

WEDNESDAY Afternoon: ( Chairs: Paul Humke and Michael Evans)

14:00Tam\'as Keleti Dynkin systems generated by large balls
14:30Pamela Pierce Functions of bounded mean variation
15:00Alexander Olevskii Approximation by almost integer translates
16:30Raymond Grinnell Functions preserving sequence spaces
17:00 J.Marshall Ash Nonuniqueness for orthonormal systems

THURSDAY Morning: ( Chairs: Jack Brown and Jack Ceder)

08:00 Nahum Zobin Whitney's problem on extendability of functions and an intrinsic metric
08:30 Richard O'Malley Universally polygonally approximable functions
09:00 Mikl\'os Laczkovich Elementary functions
10:40 James Foran Length of the graph of one-to-one functions from [0,1] onto [0,1]
11:05 Sara Jones Applications of the Baire Category Theorem
11:30 Kenneth Kellum Compositions of Darboux and connectivity functions
11:55 C.J.Neugebauer Transmission of convergence

FRIDAY Morning: ( Chairs: Jaroslav Sm\'\ital and James Foran)

08:00 Martin Dindo\vs Limits of transfinite convergent sequences of derivatives
08:30 MariannaCs\"ornyei Differentiability points of a distance function
09:00 Gyorgy Petruska Points of non-differentiability of differentiable functions
10:40 Krzysztof Ciesielski Darboux-like functions on \mathbb R^n within the classes
of Baire one, Baire two, and additive functions
11:00 U.B.Darji and MichalMorayne Level sets of typical C^n functions
11:30 Henry Fast Remarks on directional indicatrices of real functions
12:00 Robert Vallin Sub-self-similar sets and boundaries

FRIDAY Afternoon: ( Chair: Russell Gordon)

14:00 Emma D'Aniello A Stone space approach to the existence of bounded common extensions
14:30 Ian June L. Garces On the H_1 -integral
15:00 Ralph Henstock Limits of Cesaro-Perron and similar integrals

SATURDAY Morning: ( Chairs: Sara Jones and Gyuri Petruska )

08:00 Hans Volkmer The minimal Denjoy index of a symmetric perfect set
08:30 Ralph Svetic The Denjoy index and symmetric perfect sets
09:00 Pertti Mattila Menger curvature of rectifiable and fractal subsets of the plane
10:40 Mark McClure The Hausdorff dimension of Hilbert's coordinate functions
11:00 Jaroslav Sm\'\ital An omega limit set universal function on [0,1]
11:30 Zolt\'an Buczolich Real analysis and dynamics
12:00 Hongjian Shi Prevalent properties in function spaces
12:30 T.H.Steele The continuity of f\longmapsto \cup _x\in I\omega (x,f) and f\longmapsto \\omega (x,f):x\in I