Abstract
Measure theory deals with the determination of the content of geometrical configurations, or more generally, of point sets. It is directly connected with the integral calculus and set theory and finds important applications in many branches of analysis and in the foundation of probability theory. In contrast to the calculation of the areas of triangles, rectangles and other figures bounded by straight lines, figures bounded by curved lines or even more complicated ones present difficulties. Even to explain what one understands by the content of a point set is a problem. Its first solution, the concept of Riemann content, leaning heavily on the concept of the Riemann integral, was given in 1890 by Giuseppe Peano (1858–1932) and Marie Ennemond Camille Jordan (1838–1922).
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© 1975 VEB Bibliographisches Institut Leipzig
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Gellert, W., Gottwald, S., Hellwich, M., Kästner, H., Küstner, H. (1975). Measure theory. In: Gellert, W., Gottwald, S., Hellwich, M., Kästner, H., Küstner, H. (eds) The VNR Concise Encyclopedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-6982-0_36
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DOI: https://doi.org/10.1007/978-94-011-6982-0_36
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-011-6984-4
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