Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-19T07:59:36.504Z Has data issue: false hasContentIssue false

On classes of null sets

Published online by Cambridge University Press:  09 April 2009

John Lloyd
Affiliation:
Department of Mathematics, University of NewcastleNew South Wales, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Results concerning classes of null sets have been obtained by various authors. See, for example, [3], [4], [6], [7]. This paper contains results concerning classes of null sets and the notion of a ‘small system’. The motivation for considering ‘small systems’ comes from a paper by Riečan (c.f. [2]).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Halmos, P. R., Measure Theory (Van Nostrand, New York, 1950).CrossRefGoogle Scholar
[2]Riečan, B., ‘Abstract Formulation of Some Theorems of Measure Theory’, Mat.-Fyz. Časopis Slovan Akad. Vied 16, 3, (1966), 268273.Google Scholar
[3]Ficker, V., ‘Dominated Classes and Related Questions’, Acta Fac. Rerum Natur. Univ. Comenian 10, 7, (1966), 318.Google Scholar
[4]Ficker, V., ‘An Abstract Formulation of the Lebesgue Decomposition Theorem’, J. Aust. Math. Soc. 12 (1971), 101105.CrossRefGoogle Scholar
[5]Zaanen, A., Integration (North-Holland, Amsterdam, 1967).Google Scholar
[6]Sucheston, L., ‘A Note on Conservative Transformations and the Recurrence Theorem’, Amer. J. Math. 79 (1957, 444447.CrossRefGoogle Scholar
[7]Neubrunn, T., ‘Remark on Absolute Continuity of Measures’, (Russian) Mat. -Fyz. Časopis Slovan. Akad. Vied 16 (1966), 2130.Google Scholar