A decomposition theorem for locally compact groups
-
Sanjib Basu
and
Krishnendu Dutta
Abstract
We prove that, under certain restrictions, every locally compact group equipped with a nonzero, σ-finite, regular left Haar measure can be decomposed into two small sets, one of which is small in the sense of measure and the other is small in the sense of category, and all such decompositions originate from a generalised notion of a Lebesgue point. Incidentally, such class of topological groups for which this happens turns out to be metrisable. We also observe an interesting connection between Luzin sets in such spaces and decompositions of the above type.
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Articles in the same Issue
- Frontmatter
- Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound
- Isomorphism classes of weighted spaces of holomorphic functions on some subsets of complex plane
- Asymptotic behavior of solutions of fractional nabla q-difference equations
- A decomposition theorem for locally compact groups
- An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition
- Entire function sharing a small function with its mixed-operators
- Hybrid projection method for a system of unrelated generalized mixed variational-like inequality problems
- On the full transitivity of a cotorsion hull
- Comparison results for solutions of elliptic Neumann problems with lower-order terms via Steiner symmetrization
- On the formula of Cohen–Vogt relatively pointed topological semi-simplicial sets
- On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces
- On the generalized absolute convergence of Fourier series
- Embedding theorems for Besov–Morrey spaces of many groups of variables
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Projective flatness of a new class of
- Spread relation of E-valued meromorphic functions and its application
- q-dual mixed volumes and Lp-intersection bodies
