A nonseparable invariant extension of Lebesgue measure – A generalized and abstract approach
-
Sanjib Basu
and
Debasish Sen
Abstract
In this paper, we use some methods of combinatorial set theory, in particular, the ones related to the construction of independent families of sets and also some modified version of the notion of small sets originally introduced by Riečan and Neubrunn, to give an abstract and generalized formulation of a remarkable theorem of Kakutani and Oxtoby related to a nonseparable invariant extension of the Lebesgue measure in spaces with transformation groups.
Acknowledgements
We are thankful to the referee for the valuable comments which led to an overall improvement of the paper.
References
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Articles in the same Issue
- Frontmatter
- On a class of nonlinear elliptic problems with obstacle
- Higher-order commutators with power central values on rings and algebras involving generalized derivations
- A nonseparable invariant extension of Lebesgue measure – A generalized and abstract approach
- Localized boundary-domain singular integral equations of the Robin type problem for self-adjoint second-order strongly elliptic PDE systems
- On the Skitovich–Darmois theorem for complex and quaternion random variables
- Oscillation theorems for second-order delay difference equations with superlinear neutral terms
- On functions continuous with respect to a density type strong generalized topology
- A note on the trace inequality for Riesz potentials
- Degree of approximation in the space H ω p by the even-type delayed arithmetic mean of Fourier series
- Helicoidal surfaces with prescribed curvatures in a conformally flat 3-space
- On n-Hom-Leibniz algebras and cohomology
- The consistent criteria for hypotheses testing
- 𝑞-Tricomi functions and quantum algebra representations
- Continuous abstract wavelet transform on homogeneous spaces
-
Hecke
