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Appling, William D. L.

Constructive representations of certain closest approximations. (English) Zbl 0502.28006

Ann. Mat. Pura Appl., IV. Ser. 131, 187-202 (1982).
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Cited in 2 Documents

MSC:

28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
28A33 Spaces of measures, convergence of measures
46E27 Spaces of measures
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A30 Approximation by other special function classes

Keywords:

absolute continuity; integral representation, refinement continuity; real-valued bounded finitely additive functions; constructive representations of nearest points; variation norm; set function integrals
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References:

[1] Appling, W. D. L., Some integral characterizations of absolute continuity, Proc. Amer. Math. Soc, 18, 94-99 (1967) · Zbl 0146.07401
[2] Appling, W. D. L., Integral representations and refinement-unboundedness, Proc. Amer. Math. Soc, 19, 837-842 (1968) · Zbl 0159.07901
[3] Appling, W. D. L., Summability of real-valued set functions, Riv. Mat. Parma, (2), 8, 77-100 (1967) · Zbl 0177.30802
[4] Appling, W. D. L., Set functions, finite additivity and distribution functions, Ann. di Mat. pura ed applic, 96, 265-287 (1973) · Zbl 0291.28001
[5] Appling, W. D. L., Befinement continuity, Boll. U.M.I., (4), 9, 697-708 (1974) · Zbl 0325.28005
[6] Appling, W. D. L., Some continuity properties of upper and lower integral difference functionals, Ann. di Mat. pura ed applic, 101, 321-336 (1974) · Zbl 0307.28003
[7] 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
[8] Appling, W. D. L., A generalization of absolute continuity and of an analogue of the Lebesgue decomposition theorem, Riv. Mat. Univ. Parma, (3), 2, 251-276 (1973) · Zbl 0327.28007
[9] Appling, W. D. L., Integrability and closest approximation representations, Ann. di Mat. pura ed applic., 118, 217-227 (1978) · Zbl 0415.28004
[10] Kolmogoroff, A., Untersuchen über den Integralbegriff, Math. Ann., 103, 654-696 (1930) · JFM 56.0923.01
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