**Contemporary Mathematics**

Volume: 94;
1989;
326 pp;
Softcover

MSC: Primary 28;
Secondary 00

Print ISBN: 978-0-8218-5099-2

Product Code: CONM/94

List Price: $73.00

AMS Member Price: $58.40

MAA member Price: $65.70

**Electronic ISBN: 978-0-8218-7682-4
Product Code: CONM/94.E**

List Price: $73.00

AMS Member Price: $58.40

MAA member Price: $65.70

# Measure and Measurable Dynamics

Share this page *Edited by *
*R. Daniel Mauldin; R. M. Shortt; Cesar E. Silva*

Dorothy Maharam Stone's (1917-2014) contributions to operators and measure algebras has had a profound influence on this area of research. Her career, which has spanned nearly half a century, includes 40 research publications, some of them as recent as 1987. A Ph.D. student of Anna Pell Wheeler at Bryn Mawr College, Stone has been an active force in mathematics research and various professional activities.

This volume contains the proceedings of the Conference on Measure and
Measurable Dynamics, held in honor of Stone at the University of Rochester in
September 1987. The papers in this collection represent contributions from
some of the top experts in this field. Stone's work is surveyed in a number of
articles which highlight her foundational results concerning positive
operators, the characterization of homo- geneous measure algebras, and
disintegrations. In addition, there are research papers in ergodic theory,
measure theory, descriptive set theory, and the dynamics of measurable maps. A
number of the results in these papers are directly related to Stone's work.

# Table of Contents

## Measure and Measurable Dynamics

- Contents xi12 free
- Introduction xv16 free
- Biographical Note xvii18 free
- Publications of Dorothy Maharam Stone xix20 free
- List of Participants xxiii24 free
- Invariance of Rényi full conditional probabilities under group actions 126 free
- Proximal roots of minimal homeomorphisms 2348
- On the Loś-Marczewski extension of charges and its uniqueness 3560
- Marczewski null sets and intermediate Baire order 4368
- Fixed points of automorphisms of Iﭏ1 5176
- The work of Dorothy Maharam on measure theory, ergodic theory, and category algebras 5782
- Ergodic theory on homogeneous measure algebras revisited 7398
- Axiomatic characterizations of inhomogeneous Poisson point processes (IPPP) their mixtures and random translations 87112
- Uniformly distributed D-sequences 97122
- On maximal inequalities in Orlicz spaces 113138
- Finite full sets in 2-stack structure 131156
- Partial mixing, partial rigidity, and factors 141166
- A classification of disintegrations of measures 147172
- Ratio sets of endomorphisms which preserve a probability measure 159184
- An obstruction to K -fold splitting 171196
- The work of Dorothy Maharam on kernel representations of linear operators 177202
- One-to-one selections and orthogonal transition kernels 185210
- Descriptive ergodic theory 191216
- Decoding with two independent processes 207232
- Temporal and spatial distribution of closed orbits of hyperbolic dynamical systems 211236
- Nonlinear sampling of a flow 217242
- Classification problem for probability metrics 221246
- 1. Main directions in the theory of probability metrics 221246
- 2. Probability distances and probability metrics: definitions 224249
- 2.1. Some examples of metrics in probability theory 224249
- 2.2. Metric and Semimetric spaces. Distance and semidistance spaces 226251
- 2.3. Definitions of probability distance and probability metric 227252
- 2.4. Universally measurable separable metric spaces 230255
- 2.5. The equivalence of the notions of p.(semi-)distance on P2 and on x 233258

- 3. Primary, simple and compound p. distances. Minimal and maximal distances and norms 235260
- References 261286

- A new proof of Hopf's theorem on invariant measures 263288
- Markov tilings of Rn and representations of Rn actions 271296
- Groups of measurable automorphisms for spaces of finite type 291316
- A "regular oscillation" property of stable sets of measurable functions 309334
- A new proof of the strong law without first moment 315340
- Countable generators in dynamics-universal minimal models 321346