On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector
-
Alexander Kharazishvili
Abstract
It is shown that the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector can be of Lebesgue measure zero and of first Baire category. This result gives an answer to a question posed by G. Lazou.
References
[1] Bernstein F., Zur Theorie der trigonometrischen Reihe, Leipz. Ber. 60 (1908), 325–338. Suche in Google Scholar
[2] Cichon J., Kharazishvili A. and Weglorz B., Subsets of the Real Line, Wydawnictwo Uniwersytetu Lodzkiego, Lodz, 1995. Suche in Google Scholar
[3]
Hamel G.,
Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung:
[4] Kechris A. S., Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, New York, 1995. 10.1007/978-1-4612-4190-4Suche in Google Scholar
[5] Kharazishvili A. B., Nonmeasurable Sets and Functions, North-Holland Math. Stud. 195, Elsevier Science, Amsterdam, 2004. Suche in Google Scholar
[6] Kharazishvili A. B., Topics in Measure Theory and Real Analysis, Atlantis Stud. Math. 2, Atlantis Press, Paris, 2009. 10.2991/978-94-91216-36-7Suche in Google Scholar
[7] Kharazishvili A. B., Measurability properties of Vitali sets, Amer. Math. Monthly 118 (2011), no. 8, 693–703. 10.1201/b17298-11Suche in Google Scholar
[8] Kuczma M., An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, Pr. Nauk. Uniw. Śla̧skiego Katowicach 489, Uniwersytet Śla̧ski, Warsaw, 1985. Suche in Google Scholar
[9] Kuratowski K., Topology, Vol. I, Academic Press, New York, 1966. Suche in Google Scholar
[10] Miller A. W., Special subsets of the real line, Handbook of Set-Theoretic Topology, North-Holland, Amsterdam (1984), 201–233. 10.1016/B978-0-444-86580-9.50008-2Suche in Google Scholar
[11] Morgan, II J. C., Point Set Theory, Pure Appl. Math, 131, Marcel Dekker, New York, 1990. Suche in Google Scholar
[12] Oxtoby J. C., Measure and Category. A Survey of the Analogies Between Topological and Measure Spaces, Grad. Texts in Math. 2, Springer, New York, 1971. 10.1007/978-1-4615-9964-7Suche in Google Scholar
[13] Raisonnier J., A mathematical proof of S. Shelah’s theorem on the measure problem and related results, Israel J. Math. 48 (1984), no. 1, 48–56. 10.1007/BF02760523Suche in Google Scholar
[14] Shelah S., Can you take Solovay’s inaccessible away?, Israel J. Math. 48 (1984), no. 1, 1–47. 10.1007/BF02760522Suche in Google Scholar
[15] Sierpiński W., Sur la question de la mesurabilité de la base de M. Hamel, Fund. Math. 1 (1920), 105–111. 10.4064/fm-1-1-105-111Suche in Google Scholar
[16] Solovay R. M., A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1–56. 10.1142/9789812564894_0025Suche in Google Scholar
[17] Vitali G., Sul Problema Della Misura dei Gruppi di Punti di una Retta. Nota, Gamberini e Parmeggiani, Bologna, 1905. Suche in Google Scholar
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Non-trivial solutions for nonlocal elliptic problems of Kirchhoff-type
- Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
- On the modification of the Szaśz–Durrmeyer operators
- A spectral representation of the linear multivelocity transport problem
- A Tauberian theorem for the product of Abel and Cesàro summability methods
- The spaces of bilinear multipliers of weighted Lorentz type modulation spaces
- Summations of Schlömilch series containing Struve function terms
- On nondifferentiable minimax semi-infinite programming problems in complex spaces
- Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods
- On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector
- The Hardy--Littlewood maximal operator and BLO1/log class of exponents
- Bicritical domination and double coalescence of graphs
- The asymptotic behavior of a counting process in the max-scheme. A discrete case
- Functions of bounded fractional differential variation – A new concept
- Sensitivity analysis of the optimal exercise boundary of the American put option
- Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction
- A coupled system of nonlinear differential equations involving m nonlinear terms
Artikel in diesem Heft
- Frontmatter
- Non-trivial solutions for nonlocal elliptic problems of Kirchhoff-type
- Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
- On the modification of the Szaśz–Durrmeyer operators
- A spectral representation of the linear multivelocity transport problem
- A Tauberian theorem for the product of Abel and Cesàro summability methods
- The spaces of bilinear multipliers of weighted Lorentz type modulation spaces
- Summations of Schlömilch series containing Struve function terms
- On nondifferentiable minimax semi-infinite programming problems in complex spaces
- Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods
- On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector
- The Hardy--Littlewood maximal operator and BLO1/log class of exponents
- Bicritical domination and double coalescence of graphs
- The asymptotic behavior of a counting process in the max-scheme. A discrete case
- Functions of bounded fractional differential variation – A new concept
- Sensitivity analysis of the optimal exercise boundary of the American put option
- Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction
- A coupled system of nonlinear differential equations involving m nonlinear terms
