### Abstract

Let (A, A, μ) and (B, B, ν) be probability spaces, let F be a sub-σ-algebra of the product σ-algebra A× B, let X be a Banach space and let 1 < p, q< ∞. We obtain necessary and sufficient conditions in order that the conditional expectation with respect to F defines a bounded linear operator from L ^{p} (μ; L ^{q} (ν; X)) onto LFp(μ;Lq(ν;X)), the closed subspace in L ^{p} (μ; L ^{q} (ν; X)) of all functions having a strongly F-measurable representative.

Original language | English |
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Pages (from-to) | 11-19 |

Number of pages | 9 |

Journal | Positivity |

Volume | 23 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 |

### Keywords

- Conditional expectations in L (μ; L (ν; X))
- Dual of L (μ; L (ν; X))
- Radon–Nikodým property

## Fingerprint Dive into the research topics of 'On conditional expectations in L <sup>p</sup> (μ; L <sup>q</sup> (ν; X))'. Together they form a unique fingerprint.

## Cite this

^{p}(μ; L

^{q}(ν; X)).

*Positivity*,

*23*(1), 11-19. https://doi.org/10.1007/s11117-018-0589-y