On conditional mathematical expectations for functions integrable in the Pettis sense
Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 565-570
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Constructed in this note is an example of a function integrable in the Pettis sense for which no conditional mathematical expectation exists relative to some sgr-subalgebra. The example constructed shows that, in particular, the assertion of Theorem 6.1 in the M. M. Rao paper (Ref. Zh. Mat.,9B, 680, 1968) is false.
@article{MZM_1971_10_5_a11,
author = {V. I. Rybakov},
title = {On conditional mathematical expectations for functions integrable in the {Pettis} sense},
journal = {Matemati\v{c}eskie zametki},
pages = {565--570},
year = {1971},
volume = {10},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a11/}
}
V. I. Rybakov. On conditional mathematical expectations for functions integrable in the Pettis sense. Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 565-570. http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a11/