Published Online: 15 JUL 2005
Copyright © 2005 John Wiley & Sons, Ltd
Encyclopedia of Biostatistics
How to Cite
Alexander, K. S. 2005. Radon–Nikodym Theorem. Encyclopedia of Biostatistics.
- Published Online: 15 JUL 2005
The Radon–Nikodym Theorem, in the context of probability measures, states that if all events having probability 0 under one probability measure also have probability 0 under a second measure, then the second measure is obtained by integrating some density function with respect to the first measure. Applications in probability and statistics arise in the contexts of likelihood functions, conditional expectation, Girsanov's formula, spectral measures and local time. The theorem and these applications are discussed.
- Radon–Nikodym derivative;
- conditional expectation;
- Girsanov's formula