On ordinary and standard Lebesgue measures on R∞

• Autorzy: Pantsulaia G.
• Języki publikacji: EN

Abstrakty

EN

New concepts of Lebesgue measure on R∞ are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker's both measures [1], [2], Mankiewicz and Preiss-Tiser generators [6] and the measure of [4] are not = α-standard Lebesgue measures on R∞ for α = (1,1,...).

Słowa kluczowe

EN

infinite-dimensional Lebesgue measure; standard Lebesgue measure

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 3-4
• Strony: 209--222
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Pantsulaia G.

• Department of Mathematics, Georgian Technical University, Kostava St. 77, 0175 Tbilisi, Georgia,

Bibliografia

• [1] R. Baker, “Lebesgue measure” on R∞, Proc. Amer. Math. Soc. 113 (1991), 1023-1029.
• [2] R. Baker, “Lebesgue measure” on R∞. II, Proc. Amer. Math. Soc.. 132 (2004), 2577-2591.
• [3] J. Cichoń, A. Kharazishvili and B. Węglorz, Subsets of the Real Line, Wydawnictwo Uniwersytetu Łódzkiego, Łódź, 1995.
• [4] P. R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950.
• [5] G. R. Pantsulaia, Relations between shy sets and sets of νp -measure zero in Solovay’s model, Bull. Polish Acad. Sci. Math. 52 (2004), 63-69.
• [6] G. R. Pantsulaia, Invariant and Quasiinvariant Measures in Infinite-Dimensional Topological Vector Spaces, Nova Science, 2007.
• [7] G. R. Pantsulaia, On generators of shy sets on Polish topological vector spaces, New York J. Math. 14 (2008), 235-261.
• [8] G. R. Pantsulaia, Change of variable formula for “Lebesgue measures” on RN, J. Math. Sci. Adv. Appl. 2 (2009), 1-12.
• [9] D. Preiss and J. Tiser, Two unexpected examples concerning differentiability of Lipschitz functions on Banach spaces, in: Geometric Aspects of Functional Analysis (Israel, 1992-1994), Oper. Theory Adv. Appl. 77, Birkhäuser, Basel, 1995, 219-238.
• [10] R. M. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. 92 (1970), 1-56.