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Additive functions modulo a countable subgroup of ℝ

Nikos Frantzikinakis (2003)

Colloquium Mathematicae

We solve the mod G Cauchy functional equation f(x+y) = f(x) + f(y) (mod G), where G is a countable subgroup of ℝ and f:ℝ → ℝ is Borel measurable. We show that the only solutions are functions linear mod G.

Addresses

(1979)

Abstracta. 7th Winter School on Abstract Analysis

Aggregation operators and fuzzy measures on hypographs

Doretta Vivona, Maria Divari (2002)

Kybernetika

In a fuzzy measure space we study aggregation operators by means of the hypographs of the measurable functions. We extend the fuzzy measures associated to these operators to more general fuzzy measures and we study their properties.

Algebraic genericity of strict-order integrability

Luis Bernal-González (2010)

Studia Mathematica

We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space L p ( μ , X ) (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of L p ( μ , X ) (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and...

Algebraic ramifications of the common extension problem for group-valued measures

Rüdiger Göbel, R. Shortt (1994)

Fundamenta Mathematicae

Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.

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