Modular functions: Uniform boundedness and compactness |
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| Authors: | Anna Avallone Maria Antonietta Lepellere |
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| Affiliation: | (1) Dipartimento di Matematica, Università della Basilicata, via Nazario Sauro, 85, 85100 Potenza, Italy;(2) Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze, 206, 33100 Udine, Italy |
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| Abstract: | We prove the Nikodym Boundedness, Brooks-Jewett and Vitali-Hahn-Saks theorems for modular functions on orthomodular lattices with SIP and on particular complemented or sectionally complemented lattices, and the equivalence, for any complemented or sectionally complemented lattice, between the Brooks-Jewett and Vitali-Hahn-Saks theorems for group-valued modular functions. As consequence, we obtain characterizations of relative, sequential and weak compactness in spaces of modular functions. |
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