Summary
We disprove two theorems on the convergence of sequences of conditional expectations of random variables in [1] by providing a counterexample.
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Липцер, Р. Щ., Ширяев, А. Н.: Статистика plСлучайных процессов. Москва, 1974. (English translation: Liptser, R.S., Shiryayev, A.N.: Statistics of Random Processes I. New York: Springer 1978.)
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Wei-an, Z. A note on the convergence of sequences of conditional expectations of random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 53, 291–292 (1980). https://doi.org/10.1007/BF00531438
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DOI: https://doi.org/10.1007/BF00531438