On extremal extensions of regular contents and measures

Adamski, Wolfgang

doi:10.1090/S0002-9939-1994-1204367-3

On extremal extensions of regular contents and measures
HTML articles powered by AMS MathViewer

by Wolfgang Adamski PDF

Proc. Amer. Math. Soc. 121 (1994), 1159-1164 Request permission

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

Wolfgang Adamski, Extensions of tight set functions with applications in topological measure theory, Trans. Amer. Math. Soc. 283 (1984), no. 1, 353–368. MR 735428, DOI 10.1090/S0002-9947-1984-0735428-9
George Bachman and Alan Sultan, Extensions of regular lattice measures with topological applications, J. Math. Anal. Appl. 57 (1977), no. 3, 539–559. MR 427570, DOI 10.1016/0022-247X(77)90245-1
George Bachman and Alan Sultan, On regular extensions of measures, Pacific J. Math. 86 (1980), no. 2, 389–395. MR 590550
D. Bierlein and W. J. A. Stich, On the extremality of measure extensions, Manuscripta Math. 63 (1989), no. 1, 89–97. MR 975471, DOI 10.1007/BF01173704
Siegfried Graf, Induced $\sigma$-homomorphisms and a parametrization of measurable sections via extremal preimage measures, Math. Ann. 247 (1980), no. 1, 67–80. MR 565139, DOI 10.1007/BF01359867
Wolfgang Hackenbroch, Measures admitting extremal extensions, Arch. Math. (Basel) 49 (1987), no. 3, 257–266. MR 906740, DOI 10.1007/BF01271665
Wolfgang Hackenbroch, Measure extensions by conditional atoms, Math. Z. 200 (1989), no. 3, 347–352. MR 978595, DOI 10.1007/BF01215651
Jack Hardy and H. Elton Lacey, Extensions of regular Borel measures, Pacific J. Math. 24 (1968), 277–282. MR 222239
Z. Lipecki, On extreme extensions of quasi-measures, Arch. Math. (Basel) 58 (1992), no. 3, 288–293. MR 1148205, DOI 10.1007/BF01292930
Haruto Ohta and Ken-ichi Tamano, Topological spaces whose Baire measure admits a regular Borel extension, Trans. Amer. Math. Soc. 317 (1990), no. 1, 393–415. MR 946425, DOI 10.1090/S0002-9947-1990-0946425-5
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

Measures on topological spaces

Heinrich von Weizsäcker, Remark on extremal measure extensions, Measure theory, Oberwolfach 1979 (Proc. Conf., Oberwolfach, 1979) Lecture Notes in Math., vol. 794, Springer, Berlin, 1980, pp. 79–80. MR 577962