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Analysis in Integer and Fractional Dimensions (Cambridge by Ron Blei

By Ron Blei

This ebook presents an intensive and self-contained research of interdependence and complexity in settings of useful research, harmonic research and stochastic research. It makes a speciality of 'dimension' as a uncomplicated counter of levels of freedom, resulting in special family among combinatorial measurements and numerous indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. the fundamental innovations of fractional Cartesian items and combinatorial measurement are brought and associated with scales calibrated by way of harmonic-analytic and stochastic measurements. issues contain 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 aimed toward graduate scholars specialising in harmonic research, useful research or likelihood idea. It includes many routines and is appropriate 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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