Integrability and closest approximation representations. (English) Zbl 0415.28004
MSC:
| 28A25 | Integration with respect to measures and other set functions |
| 28A60 | Measures on Boolean rings, measure algebras |
Keywords:
closest approximation representations; L-summand; L-projection; C-set; integrable set functions; Banach lattice of infinitely additive measures of bounded variation on a Boolean algebra; greatest minorant; nearest approximant; bounded correspondence; games on Boolean coalition structures; Dedekind-completeReferences:
| [1] | Appling, W. D. L., A generalization of absolute continuity and of an analogue of the Lebesgue decomposition theorem, Riv. Mat. Univ. Parma, 2, 3, 251-276 (1973) · Zbl 0327.28007 |
| [2] | Appling, W. D. L., Upper and lower integral difference functionals, closest approximations, and integrability, Rend. Sem. Mat. Univ. Padova, 52, 1-24 (1974) · Zbl 0325.28006 |
| [3] | Hellinger, E., Die Orthogonalinvarianten quadratischer Formen von unendlichvielen Variablen (1907), Gottingen: Diss., Gottingen · JFM 38.0153.01 |
| [4] | Kolmogoroff, A., Untersuchungen ober den Integralbegriff, Math. Ann., 103, 654-696 (1930) · JFM 56.0923.01 · doi:10.1007/BF01455714 |
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