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Published in:
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2012 | OriginalPaper | Chapter

1. Prerequisites from Logic and Probability Theory

Author : Günther Palm

Published in: Novelty, Information and Surprise

Publisher: Springer Berlin Heidelberg

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Abstract

This chapter lays the probabilistic groundwork for the rest of the book. We introduce standard probability theory. We call the elements A of the σ-algebra “propositions” instead of “events”, which would be more common. We reserve the word “event” for the elements of the probability space Ω.

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next chapter Improbability and Novelty of Descriptions
Footnotes
1
For more details see any book on probability or measure theory, e.g., Ash (1972); Bauer (1972); Billingsley (1979); Halmos (1950); Jacobs (1978); Lamperti (1966).
 
2
\(\mathcal{B}(\Omega )\) is the smallest σ-algebra containing all open intervals \((a,b) \subseteq [0, 1]\).
 
3
see Bauer (1972) for example; p is called the Lebesgue measure.
 
Literature
.
Ash, R. B. (1972). Real analysis and probability. New York: Academic Press.
.
Bauer, H. (1972). Probability theory and elements of measure theory. New York: Holt, Rinehart and Winston.
.
Billingsley, P. (1979). Probability and measure. New York, London, Toronto: Wiley.
.
Halmos, P. R. (1950). Measure theory. Princeton: Van Nostrand.
.
Jacobs, K. (1978). Measure and integral. New York: Academic Press.
.
Lamperti, J. (1966). Probability : A survey of the mathematical theory. Reading, Massachusetts: Benjamin/Cummings.
Metadata
Title
Prerequisites from Logic and Probability Theory
Author
Günther Palm
Copyright Year
2012
Publisher
Springer Berlin Heidelberg
Book
Novelty, Information and Surprise

Print ISBN: 978-3-642-29074-9

Electronic ISBN: 978-3-642-29075-6

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-3-642-29075-6_1

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