Abstract
This chapter prepares the ground for the investigation of information transmitted by continuous signals in Chapter 10. Conceptually, the probability theory of continuous systems does not differ from the theory of discrete systems. The tools are, however, quite different, such as the theory of integral equations and of coordinate transformations.
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Reference
A Stieltjes integral is of the form (math). For a Riemann integral (math), hence it takes the form (math) Apostol, 1957, p. 191.
Ivar Fredholm (1866–1927), a Swedish mathematician.
The further generalization to Lebesgue integrals over a probability space Papoulis, 1965, p. 141 will not be made here.
Also referred to as the “sorites paradox” Blackburn, 1996, p.357.
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Kåhre, J. (2002). Continuous Systems. In: The Mathematical Theory of Information. The Springer International Series in Engineering and Computer Science, vol 684. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0975-2_9
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DOI: https://doi.org/10.1007/978-1-4615-0975-2_9
Publisher Name: Springer, Boston, MA
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