Invariant Measures

Carlos S. Kubrusly
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Carlos S. Kubrusly: Catholic University of Rio de Janeiro, Electrical Engineering Department

Chapter 13 in Essentials of Measure Theory, 2015, pp 247-267 from Springer

Abstract: Abstract A binary operation on a set X is a mapping $$\star \!: X\times X\! \rightarrow X$$ of the Cartesian product $$X\times X$$ into X. It is usual to write $$z = x \star y$$ instead of $$z = \star (x,y)$$ to indicate that z in X is the value of $$\star $$ at the point (x, y) in $$X\times X$$ . In this context it is convenient to interpret the binary operation $$\star $$ multiplicatively, so that $$x \star y$$ is interpreted as the product of x and y, and it is written in a simplified form as x y.

Keywords: Open Neighborhood; Binary Operation; Haar Measure; Borel Measure; Nonempty Interior (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-22506-7_13

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