Relations between shy sets and sets of v[p]-measure zero in Solovay's model

• Autorzy: Pantsulaia G.
• Języki publikacji: EN

Abstrakty

EN

An example of a non-zero non-atomic translation-invariant Borel measure V[p] on the Banach space l[p] (1 is less than or equal to p is less than or equal to infinity) is constructed in Solovay's model. It is established that, for 1 is less than or equal to p is less than or equal to infinity, the condition "v[p]-almost every element of l[p] has a property P" implies that "almost every" element of l[p] (in the sense of [4]) has the property P. It is also shown that the converse is not valid.

Słowa kluczowe

EN

Solovay's model; translation-invariant Borel measures; shy set; prevalent set

PL

model Solovay'a; miara Borela translacyjno-niezmiennicza

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 1
• Strony: 63--69
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Pantsulaia G.

Bibliografia

• [1] J. Cichoń, A. Kharazishvili and B. Węglorz, Subsets of the Real Line, Wyd. Uniw. Łódzkiego, Łódź, 1995.
• [2] I. V. Girsanov and B. S. Mityagin, Quasi-invariant measures in linear topological spaces, Nauchn. Dokl. Vyssh. Shkoly Fiz.-Mat. Nauki 1959, no. 2, 5-9 (in Russian).
• [3] P. R. Halmos, Measure Theory, Van Nostrand, New York, 1950.
• [4] B. R. Hunt, T. Sauer and J. A. Yorke, Prevalence: a translation-invariant „almost every" on infinite-dimensional spaces, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 217-238.
• [5] A. B. Kharazishvili, Invariant measures in Hilbert space, Soobshch. Akad. Nauk Gruzin. SSR 114 (1984), 45-48 (in Russian).
• [6] G. R. Pantsulaia, On translation-invariant measures in the non-separable Banach space l∞, Georgian Technical University Press 430 (2000), no. 2, 18-20.
• [7] R. M. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. 92 (1970), 1-56.
• [8] V. N. Sudakov, Linear sets with quasi-invariant measure, Dokl. Akad. Nauk SSSR 127 (1959), 524-525 (in Russian).
• [9] A. M. Vershik, Duality in the theory of measure in linear spaces, ibid. 170 (1966), 497-500 (in Russian).