Sub-probability measure
In the mathematical theory of probability and measure, a sub-probability measure is a measure that is closely related to probability measures. While probability measures always assign the value 1 to the underlying set, sub-probability measures assign a value smaller or equal to one to 1.
Definition
Let be a measure on the measurable space .
Properties
In measure theory, the following implications hold between measures:
So every probability measure is a sub-probability measure, but the converse is not true. Also every sub-probability measure is a finite measure and a σ-finite measure, but the converse is again not true.
gollark: <@319753218592866315>
gollark: Lisp is not over because THERE IS NO MACRON.
gollark: ?tag lyricly projects
gollark: Thus, 🦀:crab:🦀.
gollark: The second (or third, I forgot in the 20 seconds since reading the list) biggest room appears to be for Rust.
References
- Klenke, Achim (2008). Probability Theory. Berlin: Springer. p. 247. doi:10.1007/978-1-84800-048-3. ISBN 978-1-84800-047-6.
- Kallenberg, Olav (2017). Random Measures, Theory and Applications. Switzerland: Springer. p. 30. doi:10.1007/978-3-319-41598-7. ISBN 978-3-319-41596-3.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.