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 1999; 60 minutes; VHS ISBN-10: 0-8218-1351-X ISBN-13: 978-0-8218-1351-5 List Price: US$54.95 Individual Members: US$43.96 Institutional Members: US\$41.21 Order Code: VIDEO/102 This lecture examines the notion of invariant measure from a fresh viewpoint. The most familiar examples of invariant measures are area and volume, which are invariant under the group of rigid motions. Master expositor Gian-Carlo Rota shows how, starting with a few simple axioms, one can concoct new invariant measures and explore their properties. One set of such measures, known as the intrinsic volumes, are quite new and still somewhat mysterious. However, they have intriguing probabilistic interpretations and in fact can be shown to form a basis for the space of all continuous invariant measures. Rota also discusses the remarkable connection between the intrinsic volumes and the Euler characteristic. Reaching deep ideas while remaining at an elementary level, this lecture would be accessible to undergraduate mathematics majors. Reviews "This lecture examines the notion of invariant measure from a fresh viewpoint. Master expositor Gian Carlo-Rota shows how, starting with a few simple axioms, one can concoct new invariant measures and explore their properties. One set of such measures, known as the intrinsic volumes, are quite new and still somewhat mysterious. However, they have intriguing probabilistic interpretations and in fact can be shown to form a basis for the space of all continuous invariant measures. Rota also discusses the remarkable connection between the intrinsic volumes and the Euler characteristic. Reaching deep ideas while remaining at an elementary level, this lecture would be accessible to undergraduate mathematics majors." -- Zentralblatt MATH "Since this remarkable member of the mathematical community died on April 19, 1999, we are fortunate to have a visual record of his lecture. Arthur Jaffe's introductory remarks, not found in the printed article, give a summary of Rota's many accomplishments." -- Mathematical Reviews