Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On extremal extensions of regular contents and measures


Author: Wolfgang Adamski
Journal: Proc. Amer. Math. Soc. 121 (1994), 1159-1164
MSC: Primary 28A12; Secondary 28C15
DOI: https://doi.org/10.1090/S0002-9939-1994-1204367-3
MathSciNet review: 1204367
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Within the framework of regular extensions of contents and measures we show that every regular content admits an extremal extension. Under an additional assumption we can also prove the existence of extremal measure extensions.


References [Enhancements On Off] (What's this?)

  • [1] W. Adamski, Extensions of tight set functions with applications in topological measure theory, Trans. Amer. Math. Soc. 283 (1984), 353-368. MR 735428 (86c:28007)
  • [2] G. Bachman and A. Sultan, Extensions of regular lattice measures with topological applications, J. Math. Anal. Appl. 57 (1977), 539-559. MR 0427570 (55:601)
  • [3] -, On regular extensions of measures, Pacific J. Math. 86 (1980), 389-395. MR 590550 (82f:28016)
  • [4] D. Bierlein and W. J. A. Stich, On the extremality of measure extensions, Manuscripta Math. 63 (1989), 89-97. MR 975471 (89m:28007)
  • [5] S. Graf, Induced $ \sigma $-homomorphisms and a parametrization of measurable sections via extremal preimage measures, Math. Ann. 247 (1980), 67-80. MR 565139 (81d:28012)
  • [6] W. Hackenbroch, Measures admitting extremal extensions, Arch. Math. 49 (1987), 257-266. MR 906740 (88k:28005)
  • [7] -, Measure extensions by conditional atoms, Math. Z. 200 (1989), 347-352. MR 978595 (89m:28005)
  • [8] J. Hardy and H. E. Lacey, Extensions of regular Borel measures, Pacific J. Math. 24 (1968), 277-282. MR 0222239 (36:5291)
  • [9] Z. Lipecki, On extreme extensions of quasi-measures, Arch. Math. 58 (1992), 288-293. MR 1148205 (93a:28005)
  • [10] H. Ohta and K.-I. Tamano, Topological spaces whose Baire measure admits a regular Borel extension, Trans. Amer. Math. Soc. 317 (1990), 393-415. MR 946425 (90d:28016)
  • [11] D. Plachky, Extremal and monogenic additive set functions, Proc. Amer. Math. Soc. 54 (1976), 193-196. MR 0419711 (54:7729)
  • [12] V. S. Varadarajan, Measures on topological spaces, Amer. Math. Soc. Transl. Ser. 2, vol. 48, Amer. Math. Soc., Providence, RI, 1965, pp. 161-228.
  • [13] H. von Weizsäcker, Remark on extremal measure extensions, Lecture Notes in Math., vol. 794, Springer-Verlag, Berlin and New York, 1980, pp. 79-80. MR 577962 (81i:28004)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A12, 28C15

Retrieve articles in all journals with MSC: 28A12, 28C15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1204367-3
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society