Measure Theory: Proceedings of the Conference Held at Oberwolfach, 15–21 June, 1975

418 Pages·1976·4.968 MB·English

by  J. R. Choksi, R. R. Simha (auth.), Alexandra Bellow, Dietrich Kölzow (eds.)

Lecture Notes ni
Mathematics
Edited yb .A Dold dna .B Eckmann
145
Measure yroehT
Proceedings of eht Conference
Held ta Oberwolfach, 15-21 June, 1975
detidE yb .A Bellow ylremrof(
.A Ionescu )aecluT dna .D woz16K
galreV-regnirpS
Berlin.Heidelberg-
New York 1976
Editors
Alexandra Bellow
(formerly A. Ionescu Tulcea)
Department of Mathematics
Northwestern University
Evanston, Illinois 60201/USA
Dietrich KSIzow
Mathematisches Institut der
Universit~it Erlangen-NL~rnberg
BismarckstraBe 1 1/2
8520 Erlangen/BRD
Library or Congress Cataloging in PublicaUon Data
Conference on Measure Theory, Oberwolfach, Get., 1975.
Measure theory.
(Lecture notes in mathematics ; 541)
i. Measure theory--Congresses. .I Bellow,
Alexandra, 1935- II. ~dlzow, Dietrich. III. Ti-
tle. IV. Series : Lecture notes in mathematics
(Berlin) ; 541.
QA3.128 no. 541 QA312 510'.8s 515'.~2 76-40183
AMS Subject Classifivations (1970): 28-02, 46A40, 46GXX, 60-02
ISBN 3-540-07861-4 Springer-Verlag Berlin (cid:12)9 Heidelberg (cid:12)9 New York
ISBN 0-387-07861-4 Springer-Verlag New York (cid:12)9 Heidelberg (cid:12)9 Berlin
This work is subject to copyright. All rights are reserved, whether the whole
or part of the material is concerned, specifically those of translation, re-
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Under w 54 of the German Copyright Law where copies are made for other
than private use, a fee is payable to the publisher, the amount of the fee to be
determined by agreement with the publisher.
(cid:14)9 by Springer-Verlag Berlin (cid:12)9 Heidelberg 1976
Printed in Germany
Printing and binding: Beltz Offsetdruek, Hemsbach/Bergstr.
FOREWORD
This volume contains the contributions to the Conference
on Measure Theory, heldat the Research Institute for
Mathematics at Oberwolfach, from June 15 to June 21, 1975.
The organizers and theeditors would like to expresstheir
gratitude to the particlpantsfor their contributions, to
the administration of the Oberwolfach Institute for making
the Conference possible, and, last not least, to the Springer-
Verlag for its readiness to publish these Proceedings.
A. Bellow D. KSlzow
STNAPICITRAP
G. Aumann
Mathematisches Institut, Technische Universit~t M~nchen, Barerstr. 23,
8000 MHnchen ,2 Deutschland
A. Bellow (formerly Ionescu-Tulcea)
Department of Mathematics, College of Arts and Sciences, Northwestern
University, Evanston, IL 60201, USA
K. Bichteler
Department of Mathematics, University of Texas at Austin, Austin, TX
78712, USA
J. Bliedtner
Fakult~t fur Mathematik, Universit~t Bielefeld, Kurt-Schumacher-Str.
,6 4800 Bielefeld, Deutschland
V. M. Bogdan (formerly W. M. Bogdanowicz)
Department of Mathematics, Catholic University of America, Washing-
ton DC 20017, USA
.S D. Chatterji
Ecole Polytechnique F~d~rale de Lausanne, D~partement de math~matiaues,
33 Ave de Cour, 1OO7 Lausanne, Suisse
G. .Y .H Chi
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA
15260, USA
J. .R Choksi
Department of Mathematics, McGill University, Box 6070, Station A,
Montreal (101), Quebec, Canada, H3C 3GI
J. P. R. Christensen
K~benhavns Universitets Matematiske Institut, Universitetsparken ,5
2100 K~benhavn ~, Denmark
J. Diestel
Department of Mathematics, Kent State University, Kent OH 44242, USA
L. E. Dubins
Department of Mathematics, University of California at Berkeley, Ber-
keley, CA 94720, USA
.B Eifrig
Institut fHr Angewandte Mathematik, Universit~t Heidelberg, Im Neuen-
heimer Feld ,5 6900 Heidelberg, Deutschland
Vi
Th. Eisele
Institut f~r Angewandte Mathematik, Universit~t Heidelberg, Im Neuen-
heimer Feld 5 , 6900 Heidelberg, Deutschland
G. Fichera
Istituto Matematico della Universlt~ di Roma, 00185 Roma, Italia
D. H. Fremlin
Department of Mathematics, University of Essex, Colchester, Essex,
Great Britain
.Z Frollk
Matematick~ ~stav ~SAV, ~itn~ 25, 11567 Praha ,I Czechoslovakia
B. Fuchssteiner
Gesamthochschule Paderborn, Fachbereich Mathematik, Pohlweg, 4790
Paderborn, Deutschland
J. Gapaillard
Universit~ de Nantes, Institut de Math~matiques et d'Informatique,
38, Bd. Michelet, B. P. 1044, 44037 Nantes Cedex, France
M. Gattinger
Institut f~r Angewandte Mathematik, Universit~t Erlangen, Egerland-
str. 3, 8520 Erlangen, Deutschland
M. Gattinger (formerly Pehmler)
Mathematisches Institut, Universit~t Erlangen, Bismarckstr. I I/2,
8520 Erlangen, Deutschland
P. Georgiou
Department of Mathematics, University of Athens, Athens, Greece
V. Goodman
Department of Mathematics, Indiana University, Swain Hall East,
Bloomington, IN 47401, USA
.S Graf
Mathematisches Institut, Universit~t Erlangen, Bismarckstr. 1 I/2,
8520 Erlangen, Deutschland
L. Gross
Department of Mathematics, White Hall, Cornell University, Ithaca,
NY 14850, USA
M. de Guzman
Universidad de Madrid, Departamento de Ecuaciones Diferenciales, Fa-
culdad de Ciencias, C. U., Madrid 3, Espa~a
IIV
W. Hackenbroch
Fachbereich Mathematik, Universit~t Regensburg, Universit~tsstr. 31,
8400 Regensburg, Deutschland
D. Hoffmann
Fachbereich Mathematik, Universit~t Konstanz, Postfach 7733, 7750
Konstanz, Deutschland
R. E. Huff
Department of Mathematics, Pennsylvania State University, 230 Mc
Allister Bldg., University Park, PA 16802, USA
D. Eahnert
Mathematisches Institut, Universit~t Stuttgart, Pfaffenwaldring 57,
7000 Stuttgart 80, Deutschland
S. Kakutani
Department of Mathematics, Yale University, New Haven, CT 06520, USA
D. A. Kappos
Lykabetton 29, Athens 135, Greece
D. KSlzow
Mathematisches Institut, Universit~t Erlangen, Bismarckstr. 1 I/2,
8520 Erlangen, Deutschland
G. Knowles
Institut for Angewandte Mathematik und Informatik, Universit~t Bonn,
Wegelerstr. ,6 5300 Bonn, Deutschland
W. A. J. Luxemburg
California Institute of Technology, Pasadena, CA 91125, USA
G. M~gerl
Mathematisches Institut, Universit~t Erlangen, Bismarckstr. I I/2,
8520 Erlangen, Deutschland
D. Maharam-Stone
Department of Mathematics, University of Rochester, Rochester, NY
14627, USA
P. R. Masani
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA
15260, USA
K. Musia~
Institut Matematyczny PAN, PI. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
IIIV
.Z R. Pop-Stojanovic
Department of Mathematics, University of Florida, 205 Walker Hall,
Gainesville, FL 32601, USA
E. Rauch
FB ,6 Mathematik-Naturwissenschaften, Lehrstuhl fHr Mathematik IV,
Gesamthochschule Siegen, H61derlinstr. ,3 5900 Siegen-Weidenau,
Deutschland
.P Ressel
Institut fur Mathematische Stochastik, Universit~t Freiburg, Hermann-
Herder-Str. 10, 7800 Freiburg i.Br., Deutschland
M. Sion
Department of Mathematics, University of British Columbia, Vancouver
(8), Br. Columbia, Canada
D. Sondermann
Lehrstuhl .f Theoretische Volkswirtschaftslehre, Universit~t Hamburg,
von Melle Park 15, 2000 Hamburg 13, Deutschland
T. P. Srinivasan
Department of Mathematics, University of Kansas, Lawrence, KS 66045,
USA
A. H. Stone
Department of Mathematics, University of Rochester, Rochester, NY
14627, USA
W. Strauss
Mathematisches Institut A, Universit~t Stuttgart, Pfaffenwaldring 57,
7000 Stuttgart 80, Deutschland
G. .E F. Thomas
Rijksuniversiteit Groningen, Mathematisch Instituut, Hoogbouw WSN,
Universiteitscomplex Paddepool, Postbus 800, Groningen, Nederland
F. Tops~e
K~benhavns Universitets Matematiske Institut, Universitetsparken ,5
2100 K~benhavn ~, Dent/ark
.T Traynor
Department of Mathematics, University of Windsor, Windsor, Ontario,
Canada, N9B 3P4
.H von WeizsMcker
Mathematisches Institut, Universit~t M~nchen, Theresienstr. 39,
8000 MOnchen ,2 Deutschland
XI
J. D. M. Wright
9OA Bulmershe Rd., Berkshire, Reading, England
A. C. Zaanen
Mathematisch Instituut, Rijksuniversiteit te Leiden, Wassenaarseweg
80, Leiden, Nederland
CONTRIBUTIONS
General Measure Theory
J.R. CHOKSI - R.R. SIMHA:
Set and Point Transformations on Homogeneous Spaces I
(communicated by J.R. CHOKSI)
K.-TH. EISELE:
On the Uniqueness of Preimages of Measures 5
(submitted as manuscript)
D. FREMLIN:
Pointwise Compact Sets of Measurable Functions
(excerpt from Manuscr. Math. 15 (1975), 219-242)
D. KAHNERT:
Haar-MaB und Hausdorff-MaB 13
J. L. KELLEY - T.P. SRINIVASAN:
A Unified Proof of Fubini Theorem for Baire and Borel Measure 25
(submitted as manuscript)
K. MUSIA~:
Inheritness of Compactness and Perfectness of Measures by 31
Thick Subsets
A.H. STONE:
Topology and Measure Theory 43
Finitely Additive Measures
J.P.R. CHRISTENSEN:
Submeasures and the Problem on the Existence of Control Measures 49
L.E. DUBINS:
On Disintegration and Conditional Probabilities 53
D. MAHARAM:
Finitely Additive Measures on the Integers
(to appear elsewhere)
Vector Valued Measures
G. KNOWLES:
On Liapunov Vector Measures 61
P. MASANI:
Measurability and Pettis Integration in Hilbert Spaces 69
IIX
M.K. NAYAK - T.P. SRINIVASAN:
Vector Valued Inner Measures 107
(submitted as manuscript)
G.E.F. THOMAS:
Totally Summable Functions with Values in Locally Convex 117
Spaces
Liftin~s
B. EIFRIG:
Ein Nicht-Standard-Beweis fur die Existenz eines Liftings 133
(submitted as manuscript)
J. GAPAILLARD:
Rel~vements sur une Alg~bre d'Ensembles 137
(submitted as manuscript)
S. GRAF - H. VON WEIZS~CKER:
On the Existence of Lower Densities in Noncomplete Measure 155
Spaces
(submitted as manuscript)
W. STRAUSS:
Beschr~nkte lineare Liftings
(published in Bull. Acad. Polon. Sci., S~r. math. astron.
phys. 23 (1975), 27-33)
T. Traynor:
An Elementary Proof of the Lifting Theorem
(published in Pacific J. Math. 53 (1974), 267-272)
H. VON WEIZS~CKER:
Some Negative Results in the Theory of Lifting 159
Differentiation of Measures
S.D. CHATTERJI: 173
Differentiation of Measures
M. DE GUZMAN: 181
Differentiation of Integrals in ~n
F. TOPS~E:
Packings and Coverings with Balls in Finite Dimensional Normed 187
Spaces
Radon-Nikod~m Theorems for Vector Valued Measures
G.Y.H. CHI: 199
On the Radon-Nikodym Theorem in Locally Convex Spaces