On monogenic operators and measures
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- by Z. Lipecki and D. Plachky PDF
- Proc. Amer. Math. Soc. 82 (1981), 216-220 Request permission
Abstract:
The notion of a monogenic operator between linear lattices, generalizing that of a monogenic measure, is introduced and investigated. The decomposition of an operator into its monogenic and antimonogenic parts is established. Products of monogenic measures are also considered.References
- Albert Ascherl and Jürgen Lehn, Two principles for extending probability measures, Manuscripta Math. 21 (1977), no. 1, 43–50. MR 453951, DOI 10.1007/BF01176900
- Sterling K. Berberian, Measure and integration, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1965. MR 0183839
- Graham Jameson, Ordered linear spaces, Lecture Notes in Mathematics, Vol. 141, Springer-Verlag, Berlin-New York, 1970. MR 0438077
- Roy A. Johnson, Some types of Borel measures, Proc. Amer. Math. Soc. 22 (1969), 94–99. MR 248313, DOI 10.1090/S0002-9939-1969-0248313-3
- Z. Lipecki, D. Plachky, and W. Thomsen, Extensions of positive operators and extreme points. I, Colloq. Math. 42 (1979), 279–284. MR 567564, DOI 10.4064/cm-42-1-279-284 W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. I, North-Holland, Amsterdam, 1971.
- J. Łoś and E. Marczewski, Extensions of measure, Fund. Math. 36 (1949), 267–276. MR 35327, DOI 10.4064/fm-36-1-267-276 E. Marczewski (Szpilrajn), On absolutely measurable sets and functions, C. R. Soc. des Sciences et des Lettres de Varsovie 30 (1937), 39-67. (Polish, French summary)
- E. Marczewski and C. Ryll-Nardzewski, Remarks on the compactness and non direct products of measures, Fund. Math. 40 (1953), 165–170. MR 59996, DOI 10.4064/fm-40-1-165-170
- Alvin F. Martin, A note on monogenic Baire measures, Amer. Math. Monthly 84 (1977), no. 7, 554–555. MR 473128, DOI 10.2307/2320023
- Detlef Plachky, Extremal and monogenic additive set functions, Proc. Amer. Math. Soc. 54 (1976), 193–196. MR 419711, DOI 10.1090/S0002-9939-1976-0419711-3 H. L. Royden, Real analysis, London, 1970.
- V. S. Varadarajan, Groups of automorphisms of Borel spaces, Trans. Amer. Math. Soc. 109 (1963), 191–220. MR 159923, DOI 10.1090/S0002-9947-1963-0159923-5
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 216-220
- MSC: Primary 47B55; Secondary 28A99
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609654-6
- MathSciNet review: 609654