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By Ron Blei

This publication offers an intensive and self-contained research of interdependence and complexity in settings of useful research, harmonic research and stochastic research. It specializes in 'dimension' as a easy counter of levels of freedom, resulting in special family members among combinatorial measurements and numerous indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. the fundamental suggestions of fractional Cartesian items and combinatorial measurement are brought and associated with scales calibrated by way of harmonic-analytic and stochastic measurements. issues comprise the (two-dimensional) Grothendieck inequality and its extensions to raised dimensions, stochastic versions of Brownian movement, levels of randomness and Frechet measures in stochastic research. This ebook is essentially geared toward graduate scholars specialising in harmonic research, sensible research or likelihood thought. It includes many routines and is acceptable for use as a textbook. it's also of curiosity to scientists from different disciplines, together with laptop scientists, physicists, statisticians, biologists and economists.

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