Conditional Expectation in an Uncertainty Space
In the classical (probability) setting, the Radon-Nikodym Theorem is used to prove the existence of conditional expectations. This paper states the Radon-Nikodym Theorem for uncertain measures which were introduced by Liu (2007) to model belief degrees. This version of the theorem is adapted from Graf (1980) who established the theorem for non-additive measures called capacities. This paper then uses the theorem to define the conditional expectation of an uncertain variable with respect to a σ-algebra. Properties of the conditional expectation are established.
Aujero, E., Frondoza, M., De Lara-Tuprio, E., Eden, R., & Teng, T. R. (2019, February). Conditional Expectation in an Uncertainty Space. In Journal of Physics: Conference Series (Vol. 1180, No. 1, p. 012003). IOP Publishing.