Abstract
We briefly introduce some mathematical concepts and associated important theorems that will be used in the subsequent chapters to study the semantics of probabilistic processes. The main topics covered in this chapter include the Knaster–Tarski fixed-point theorem, continuous functions over complete lattices, induction and coinduction proof principles, compact sets in topological spaces, the separation theorem, the Banach fixed-point theorem, the π-λ theorem and the duality theorem in linear programming. Most of the theorems are stated without proofs because they can be found in many textbooks.
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Winskel, G.: The Formal Semantics of Programming Languages: an Introduction. The MIT Press, Cambridge (1993)
Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge University Press, Cambridge (2012)
Matoušek, J.: Lectures on Discrete Geometry. Springer, New York (2002)
Billingsley, P.: Probability and Measure. Wiley, New York (1995)
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© 2014 Shanghai Jiao Tong University Press, Shanghai and Springer-Verlag Berlin Heidelberg
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Deng, Y. (2014). Mathematical Preliminaries. In: Semantics of Probabilistic Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45198-4_2
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DOI: https://doi.org/10.1007/978-3-662-45198-4_2
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-662-45198-4
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