Existence of Infinite Product Measures

2017/05/03 by Juan Carlos Sampedro, Sampedro, Juan Carlos
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1705.01621

openalex publication_date 2017/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the existence of product measures in an elementary manner. Moreover, the L_p spaces of this measures are simplified in terms of finite product measures following the approach of [21]. This decomposition simplifies infinite dimensional integration and gives to this theory a computational framework.

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