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Let X be a Banach function space over a nonatomic probability space. The quasiBanach space weak–X is defined in a natural way. We give some necessary and sufficient conditions on X for all the conditional expectation operators to be uniformly bounded operators from X into weak–X . Mathematics subject classification (2010): 46E30, 47B38, 60G42.

Uniform boundedness of conditional expectation operators on a Banach function space