Exchange

Updated: October, 1998

Report on the

(

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

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:**

Introduction by Richard O'Malley

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

08:10 * Brian Thomson*Some
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*)

14:00 *Tam\'as Keleti*
Dynkin systems generated by large balls
14:30 *Pamela Pierce*
Functions of bounded mean variation
15:00 *Alexander Olevskii*
Approximation by almost integer translates 16:30 *Raymond 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