Category and Measure

Infinite Combinatorics, Topology and Groups

Inbunden, Engelska, 2025

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Topological spaces in general, and the real numbers in particular, have the characteristic of exhibiting a 'continuity structure', one that can be examined from the vantage point of Baire category or of Lebesgue measure. Though they are in some sense dual, work over the last half-century has shown that it is the former, topological view, that has pride of place since it reveals a much richer structure that draws from, and gives back to, areas such as analytic sets, infinite games, probability, infinite combinatorics, descriptive set theory and topology. Keeping prerequisites to a minimum, the authors provide a new exposition and synthesis of the extensive mathematical theory needed to understand the subject's current state of knowledge, and they complement their presentation with a thorough bibliography of source material and pointers to further work. The result is a book that will be the standard reference for all researchers in the area.

Produktinformation

Utgivningsdatum2025-01-23
Mått157 x 235 x 23 mm
Vikt652 g
FormatInbunden
SpråkEngelska
SerieCambridge Tracts in Mathematics
Antal sidor345
FörlagCambridge University Press
ISBN9780521196079

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N. H. Bingham is Emeritus Professor at Imperial College London. He is a probabilist with interests also in analysis, statistics, financial mathematics and history of mathematics, all of which he has taught extensively. He has written more than 160 papers and three books, and edited three others. Adam J. Ostaszewski is Professor at the London School of Economics. His research interests span set theory and topology (where he is known for Ostaszewski's clubs and Ostaszewski's space), and applications of real analysis to probability, economics and accounting. He is the author of more than 100 papers and three books.

Prologue. Regular variation; 1. Preliminaries; 2. Baire category and related results; 3. Borel sets, analytic sets and beyond: $\Delta^1_2$; 4. Infinite combinatorics in $\mathbb{R}^n$: shift-compactness; 5. Kingman combinatorics and shift-compactness; 6. Groups and norms: Birkhoff–Kakutani theorem; 7. Density topology; 8. Other fine topologies; 9. Category-measure duality; 10. Category embedding theorem and infinite combinatorics; 11. Effros' theorem and the cornerstone theorems of functional analysis; 12. Continuity and coincidence theorems; 13. * Non-separable variants; 14. Contrasts between category and measure; 15. Interior point theorems: Steinhaus–Weil theory; 16. Axiomatics of set theory; Epilogue. Topological regular variation; References; Index.