On the inner Daniell-Stone and Riesz representation theorems
- 1.1k Downloads
The paper deals with the context of the inner Daniell- Stone and Riesz representation theorems, which arose within the new development in measure and integration in the book 1997 and subsequent work of the author. The theorems extend the traditional ones, in case of the Riesz theorem to arbitrary Hausdorff topological spaces. The extension enforces that the assertions attain different forms. The present paper wants to exhibit special situations in which the theorems retain their familiar appearance.
KeywordsInner extensions inner premeasures Radon measures Radon premeasures positive (=isotone) linear functionals inner sources inner preintegrals Radon preintegrals tightness theorem of Kisyński
Unable to display preview. Download preview PDF.
- 1.N. Bourbaki, Intégration, Chap. IX. Hermann 1969.Google Scholar
- 3.H. König, Measure and Integration: An Advanced Course in Basic Procedures and Applications. Springer 1997.Google Scholar
- 5.H. König, What are signed contents and measures? Math.Nachr. 204 (1999), 101-124.Google Scholar
- 10.H. König, Upper envelopes of inner premeasures. To appear in Annales Inst. Fourier.Google Scholar
- 11.A. V. Mikhalev and V. K. Zakharov, Solution of Riesz-Radon Problem. In: Intern. Congress Math. Berlin 1998, Abstracts of Short Comm. and Poster Sess., pp. 141-142.Google Scholar
- 15.V. K. Zakharov and A.V. Mikhalev, The problem of integral representation for Radon measures on a Hausdorff space (in Russian). Doklady Akad. Nauk 360 (1998), 13-15. English translation in Doklady Math. 57 (1998), 337-339.Google Scholar
- 17.V. K. Zakharov, A solution of the general Riesz-Radon problem for a Hausdorff space. In: Intern.Congress Math. Berlin 1998, Abstracts of Short Comm. and Poster Sess., p.166.Google Scholar