Abstract
We define the integral of semicontinuous functions, and consider properties of such integrals, like Fubini’s theorem. Volumes of compact sets are defined, and certain rules, like Cavalieri’s principle, for their computation are given. In particular, computations simplify in rotationally symmetric situations.
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© 1998 Springer-Verlag Berlin Heidelberg
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Jost, J. (1998). The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets. In: Postmodern Analysis. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03635-8_14
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DOI: https://doi.org/10.1007/978-3-662-03635-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63485-0
Online ISBN: 978-3-662-03635-8
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