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On the coronary coronary heart of this monograph is the Brunn–Minkowski precept, which may be utilized to good impact in studying such ideas as amount and flooring area and their generalizations. Notably, the notions of mixed amount and mixed area measure come up naturally and the basic inequalities that are glad by mixed volumes are thought-about proper right here intimately. The author presents an entire introduction to convex our our bodies, along with full proofs for some deeper theorems. The book provides hints and ideas that would connections with totally different fields and an exhaustive reference itemizing. This second model has been considerably expanded to reflect the speedy developments of the earlier 20 years. It consists of new chapters on valuations on convex our our bodies, on extensions identical to the Lp Brunn–Minkowski precept, and on affine constructions and inequalities. There are moreover many dietary dietary supplements and updates to the distinctive chapters, and a substantial enlargement of chapter notes and references.
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