Summary
By means of continuity properties of upper and lower integral difference functionals, characterizations are obtained of absolute continuity of finitely additive non negative-valued set functions and continuity of real-valued functions defined onℝ N.
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References
W. D. L. Appling,Some Integral Characterizations of Absolute Continuity, Proc. Amer. Math. Soc.,18 (1967), pp. 94–99.
W. D. L. Appling,Summability of Real-Valued Set Functions, Riv. Mat. Parma,8 (1967), pp. 77–100.
W. D. L. Appling,Integral Representations and Refinement-Unboundedness, Proc. Amer. Math. Soc.,19 (1968), pp. 837–842.
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A. Kolmogoroff,Untersuchungen über den Integralbegriff, Math. Ann.,103 (1930), pp. 654–696.
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Entrata in Redazione il 6 febbraio 1973.
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Appling, W.D.L. Some continuity properties of upper and lower integral difference functionals. Annali di Matematica 101, 321–336 (1974). https://doi.org/10.1007/BF02417111
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DOI: https://doi.org/10.1007/BF02417111