On general characterization of Young measures associated with Borel\n functions

2016/01/02 by Andrzej Z. Grzybowski, Grzybowski, Andrzej Z., Piotr Puchała +1
Mathematics · #46N10 #46N30 #49M30 #60A10 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1601.00206

openalex publication_date 2016/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Young measure associated with a Borel function f is a\nprobability distribution of the random variable f(U), where U has a uniform\ndistribution on the domain of f. As an auxiliary result, the fact that Young\nmeasures associated with simple functions are weak* dense in the set of Young\nmeasures associated with measurable functions is proved. Finally some examples\nof specific applications of the main result are presented with comments.\n

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