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RESEARCH PRODUCT

Sobolev Calculus on Metric Measure Spaces

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Several different approaches to the theory of weakly differentiable functions over abstract metric measure spaces made their appearance in the literature throughout the last twenty years. Amongst them, we shall mainly follow the one (based upon the concept of test plan) that has been proposed by Ambrosio, Gigli and Savare. The whole Sect. 2.1 is devoted to the definition of such notion of Sobolev space W1, 2(X) and to its most important properties.