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Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.
Okada, S., and Ricker, W. J.. "Fréchet-spaces-valued measures and the AL-property.." RACSAM 97.2 (2003): 305-314. <http://eudml.org/doc/40978>.
@article{Okada2003, abstract = {Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.}, author = {Okada, S., Ricker, W. J.}, journal = {RACSAM}, keywords = {Espacios de Fréchet; Medidas vectoriales; Retículo de Banach; Fréchet space; vector measure; AL-property; integration operator}, language = {eng}, number = {2}, pages = {305-314}, title = {Fréchet-spaces-valued measures and the AL-property.}, url = {http://eudml.org/doc/40978}, volume = {97}, year = {2003}, }
TY - JOUR AU - Okada, S. AU - Ricker, W. J. TI - Fréchet-spaces-valued measures and the AL-property. JO - RACSAM PY - 2003 VL - 97 IS - 2 SP - 305 EP - 314 AB - Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm. LA - eng KW - Espacios de Fréchet; Medidas vectoriales; Retículo de Banach; Fréchet space; vector measure; AL-property; integration operator UR - http://eudml.org/doc/40978 ER -