Some properties of Vitali sets
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Surinder Pal Singh Kainth
and
Narinder Singh
Abstract
If
Funding source: University Grants Commission, INDIA
Award Identifier / Grant number: 1033/(CSIR-UGC NET DEC. 2016)
Funding statement: Narinder Singh is supported by UGC India with Ref. No. 1033/(CSIR-UGC NET DEC. 2016).
References
[1] P. R. Halmos, Measure Theory, D. Van Nostrand, New York, 1950. 10.1007/978-1-4684-9440-2Search in Google Scholar
[2] S. P. S. Kainth, Null subsets of all sizes inside Vitali sets, Amer. Math. Monthly 127 (2020), no. 8, 743–743. 10.1080/00029890.2020.1785806Search in Google Scholar
[3] A. B. Kharazishvili, Measurability properties of Vitali sets, Amer. Math. Monthly 118 (2011), no. 8, 693–703. 10.1201/b17298-11Search in Google Scholar
[4] C. S. Kubrusly, Essentials of Measure Theory, Springer, Cham, 2015. 10.1007/978-3-319-22506-7Search in Google Scholar
[5] I. K. Rana, An Introduction to Measure and Integration, 2nd ed., Grad. Stud. Math. 45, American Mathematical Society, Providence, 2002. 10.1090/gsm/045Search in Google Scholar
[6] S. Shirali and H. L. Vasudeva, Metric Spaces, Springer, London, 2006. Search in Google Scholar
[7] A. P. Solodov, On the limits of the generalization of the Kolmogorov integral (in Russian), Mat. Zametki 77 (2005), no. 2, 258–272; translation in Math. Notes 77 (2005), no. 1–2, 232–245. 10.1007/s11006-005-0023-1Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
Articles in the same Issue
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
