M-Cantorvals of Ferens type
-
Michał Banakiewicz
and
Franciszek Prus-Wiśniowski
Abstract
A special family of multigeometric series is considered from the point of view of behaviour of their sets of subsums. A sufficient condition for their sets of subsums to be M-Cantorvals is proven. The Lebesgue measure of those special M-Cantorvals is computed and it is shown to be equal to the sum of lengths of all component intervals of the M-Cantorvals. A new sufficient condition for the set of subsums of a series to be a Cantor set is formulated and it is used to demonstrate that the discussed multigeometric series always have Cantor sets as their sets of subsums for sufficiently small ratios of the series.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Outer measure on effect algebras
- Hamiltonian ordered algebras and congruence extension
- Automorphism groups with some finiteness conditions
- Only finitely many Tribonacci Diophantine triples exist
- Abundant semigroups with a *-normal idempotent
- Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses
- Monotonicity results for delta fractional differences revisited
- M-Cantorvals of Ferens type
- Comparison of ψ-porous topologies
- On certain generalized matrix methods of convergence in (ℓ)-groups
- Some applications of first-order differential subordinations
- Hankel determinant for a class of analytic functions involving conical domains defined by subordination
- Nonoscillation and exponential stability of the second order delay differential equation with damping
- Positive solutions of perturbed nonlinear hammerstein integral equation
- Ricci solitons on 3-dimensional cosymplectic manifolds
- Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups
- The super socle of the ring of continuous functions
- On the internal approach to differential equations 2. The controllability structure
- Finiteness of the discrete spectrum in a three-body system with point interaction
- On a subclass of Bazilevic functions
