Abstract
“If a sequentially point continuous submeasure (Maharam submeasure) defined on a measurable space admits a control measure, then a Fubini condition is fulfilled for measurable subsets of the product of the space with the unit interval (with usual Lebesgue measure). The main result is that this Fubini condition is also sufficient for the existence of control measure. Some related results are proved.”
Keywords
- Measurable Space
- Boolean Algebra
- Convex Combination
- Measurable Subset
- Normalize Lebesgue Measure
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References
Jens Peter Reus Christensen, Topology and Borel structure, Notas de matematica nr. 10, North-Holland.
J.P.R. Christensen & Wojchiech Herer, On the existence of pathological submeasures and the construction of exotic groups, Math. Ann. 213, 203–210 (1975).
Maharam D., An algebraic characterization of measure algebras, Ann. Math. 48, 154–157 (1947).
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© 1978 Springer-Verlag
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Christensen, J.P.R. (1978). Some results with relation to the control measure problem. In: Aron, R.M., Dineen, S. (eds) Vector Space Measures and Applications II. Lecture Notes in Mathematics, vol 645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069660
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DOI: https://doi.org/10.1007/BFb0069660
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08669-7
Online ISBN: 978-3-540-35903-6
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