## Jordan decompositions of generalised vector measures |

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### Contents

Contents | 1 |

Riesz Spaces of Additive Functions | 30 |

Banach Lattices of Additive Functions | 55 |

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### Common terms and phrases

additive vector measures Af-singular Aliprantis and Burkinshaw AM-space with unit band decompositions Boolean algebra Boolean ring bounded additive functions bounded disjoint sequence bounded operators bounded vector measures cancellation property commutative minimal clan compact operators complete Banach lattice complete Riesz space decomposition of order decomposition of vector define E+ satisfying following are equivalent follows from Lemma follows from Theorem fuzzy sets G E+ G is order G o6a(E hence holds Jordan decomposition L-weakly lattice-ordered group Let G linear operator locally bounded variation locally compact locally strongly additive M-normed Nakano space norm complete norm Lebesgue decomposition normed Riesz space oba(E oba(E,G order bounded additive order bounded disjoint order bounded sequences order bounded vector order complete AM-space order complete Banach order complete Riesz order continuous norm order direct sum order Lebesgue decomposition ordered vector space partial differential equations projection bands Proof Schmidt semigroup spaces and projection strongly additive vector U-bounded weakly compact yields