2017/10/05 by Moritz Schönherr, Schönherr, Moritz, Friedemann Schuricht +1
Computer Science · Engineering · Mathematics · #28-02 #Advanced Numerical Analysis Techniques #Digital Image Processing Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1710.02197
openalex publication_date 2017/10/05 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28
Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The main results presented here are a more precise representation of the dual of the space of essentially bounded functions, leading to the notion of pure measures, and the definition and analysis of density measures which constitute a large class of such measures. It is shown that density measures have applications in the context of traces. In particular, new and meaningful examples of pure measures are given on Rn, in contrast to common examples in the literature, which are usually constructed on N.