A general measure extension procedure

Sultan, Alan

doi:10.1090/S0002-9939-1978-0466469-X

A general measure extension procedure
HTML articles powered by AMS MathViewer

by Alan Sultan PDF

Proc. Amer. Math. Soc. 69 (1978), 37-45 Request permission

Abstract:

We give a very general and flexible way of producing measure extensions. We obtain as corollaries many well-known and important measure extension and integral representation theorems as well as the main theorems of several recent papers.

References

A. D. Alexandroff, Additive set-functions in abstract spaces, Rec. Math. [Mat. Sbornik] N. S. 8 (50) (1940), 307–348 (English, with Russian summary). MR 0004078
A. D. Alexandroff, Additive set-functions in abstract spaces, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 563–628 (English, with Russian summary). MR 0005785
Richard A. Alò and Harvey L. Shapiro, Normal topological spaces, Cambridge Tracts in Mathematics, No. 65, Cambridge University Press, New York-London, 1974. MR 0390985
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, Regular lattice measures: mappings and spaces, Pacific J. Math. 67 (1976), no. 2, 291–321. MR 507538

Measure theoretic techniques in topology and mappings of replete and measure replete spaces

Sterling K. Berberian, Measure and integration, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1965. MR 0183839
S. K. Berberian, On the extension of Borel measures, Proc. Amer. Math. Soc. 16 (1965), 415–418. MR 176022, DOI 10.1090/S0002-9939-1965-0176022-4
Jack Hardy and H. Elton Lacey, Extensions of regular Borel measures, Pacific J. Math. 24 (1968), 277–282. MR 222239
R. B. Kirk, Algebras of bounded real-valued functions. I, Nederl. Akad. Wetensch. Proc. Ser. A 75=Indag. Math. 34 (1972), 443–451. MR 0320725
R. B. Kirk and J. A. Crenshaw, A generalized topological measure theory, Trans. Amer. Math. Soc. 207 (1975), 189–217. MR 369648, DOI 10.1090/S0002-9947-1975-0369648-7
Jan Mařík, The Baire and Borel measure, Czechoslovak Math. J. 7(82) (1957), 248–253 (English, with Russian summary). MR 88532
M. A. Naĭmark, Normed rings, Reprinting of the revised English edition, Wolters-Noordhoff Publishing, Groningen, 1970. Translated from the first Russian edition by Leo F. Boron. MR 0355601
A. Sultan, General rings of functions, J. Austral. Math. Soc. Ser. A 20 (1975), no. 3, 359–365. MR 388348, DOI 10.1017/s1446788700020711
Alan Sultan, Measure, compactification and representation, Canadian J. Math. 30 (1978), no. 1, 54–65. MR 464168, DOI 10.4153/CJM-1978-005-5
Flemming Topsøe, Topology and measure, Lecture Notes in Mathematics, Vol. 133, Springer-Verlag, Berlin-New York, 1970. MR 0422560

Measures on topological spaces

48