By Ron Blei

This booklet offers a radical and self-contained research of interdependence and complexity in settings of practical research, harmonic research and stochastic research. It specializes in 'dimension' as a easy counter of levels of freedom, resulting in distinct relatives among combinatorial measurements and diverse 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. themes comprise the (two-dimensional) Grothendieck inequality and its extensions to better dimensions, stochastic versions of Brownian movement, levels of randomness and Frechet measures in stochastic research. This publication is essentially aimed toward graduate scholars specialising in harmonic research, sensible research or likelihood conception. It comprises many routines and is acceptable for use as a textbook. it's also of curiosity to scientists from different disciplines, together with desktop scientists, physicists, statisticians, biologists and economists.

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Analysis in Integer and Fractional Dimensions (Cambridge Studies in Advanced Mathematics) by Ron Blei

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