Category and Measure

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.