by Y Yamasaki (Kyoto)

This book is based on lectures given at Yale and Kyoto Universities and provides a self-contained detailed exposition of the following subjects: 1) The construction of infinite dimensional measures, 2) Invariance and quasi-invariance of measures under translations. This book furnishes an important tool for the analysis of physical systems with infinite degrees of freedom (such as field theory, statistical physics and field dynamics) by providing material on the foundations of these problems.

• Part A:
  • Extendability of a Family of Measures to a σ-Additive Measure (Kolmogorov-Bochner-Minlos Theory)
  • Direct Product and Projective Limit
  • Measures on Vector Spaces
  • Definition on Nuclearity without Using Hilbertian Semi-Norms
• Part B:
  • Invariance and Quasi-Invariance of Measures on Infinite Dimensional Spaces
  • Invariant Measure on a Group
  • Gaussian Measures and Related Problems
  • The Set Y_μ of All Quasi-Invariant Translations
  • Product Measures on IR^∞, IR₀^∞-Invariant Measures on IR^∞