Nilpotent Structures in Ergodic Theory

Bryna Kra and Bernard Host  
Comments and corrections welcome.  

  • June 19, 2018: Fuurther small corrections throughout.Comments and corrections are welcome.   PDF AVAILABLE HERE 
  • March 19, 2018: Further small corrections throughout and a new chapter adding, completing the proof of the Structure Theorem. Comments and corrections are welcome.    
  • March 5, 2018: Numerous typos corrected, rewritten introduction, and additions in several chapters. Comments and corrections are welcome.    
  • January 30, 2018: Numerous corrections in all chapters and notation changes thoughout. Comments and corrections are welcome.    
  • December 9, 2017: Further correction of errors in early chapters, and the remaining chapters are added.  
  • November 8, 2017: Further correction of errors in early chapters, and two new cchapters (on the use of characteristic factors and on uniformity seminorms) are added. The table of contents includes further chapters that will be added soon, and these may change. Comments and corrections are welcome.  
  • September 26, 2017: Numerous typos corrected and further examples added. The table of contents includes further chapters that will be added soon, and these may change. Comments and corrections are welcome.    
  • September 20, 2017: New chapters added include other structural results and a proof of the Ergodic Structure Theroem. The table of contents includes further chapters that will be added soon, but these may change. Comments and corrections are welcome.    
  • August 22, 2017: This is a preliminary version of our book. Chapters included here cover background material, cubic structures, nilsystems, and an overview of the structure theorem. The table of contents includes further chapters that will be added soon, but these may change.