Abstract
This chapter is devoted to the construction and properties of the conditional expectation with respect to a sub-σ-field. In the first section, we discuss the discrete setting, which helps to understand the axiomatic definition of conditional expectation in the general case. The last section introduces the notion of conditional law, which is useful in this book mainly from a conceptual point of view.
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References
Kallenberg, O., Foundations of modern probability. Probability and its Applications. 2nd ed. Springer, 2002.
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Le Gall, JF. (2022). Conditioning. In: Measure Theory, Probability, and Stochastic Processes. Graduate Texts in Mathematics, vol 295. Springer, Cham. https://doi.org/10.1007/978-3-031-14205-5_11
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DOI: https://doi.org/10.1007/978-3-031-14205-5_11
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