Some Properties of Algebras of Real-valued Measurable Functions
Measures and measurable functions are used primarily as tools for carrying out various calculations to increase our knowledge. We learn how to combine them in various ways by studying real analysis; a very useful subject on which very much has been written. In this paper, we regard measurable functions as algebras of real-valued functions (or equivalence classes of them) on a set or topological space under point-wise addition, multiplication, or lattice operations and our techniques resemble closely those used to study algebras of continuous functions. This is done by examining a number of explicit examples including Borel and Lebesgue measures and measurable functions.
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Azadi, H.; Henriksen, Melvin; Momtahan, Ehsan. Some properties of algebras of real-valued measurable functions. Acta Math. Hungar.. 124 (2009), no. 1, 15–23. DOI: 10.1007/s10474-009-8138-6