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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 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.
References
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.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Palm, G. (2012). Prerequisites from Logic and Probability Theory. In: Novelty, Information and Surprise. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29075-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-29075-6_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29074-9
Online ISBN: 978-3-642-29075-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)