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In martingale theory, various Banach spaces (of martingales) are considered. Analysis of such spaces are very importnat. For a Banach function space X over a nonatomic probbility space, one can associate two Banach spaces of martingales. We give some necessary and sufficient condition on X for these two Banach spaces to be the same.

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This page is a summary of: On some Banach spaces of martingales associated with function spaces, Forum Mathematicum, January 2012, De Gruyter,
DOI: 10.1515/form.2011.083.
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