A general result on the equivalence between derivation of integrals and weak inequalities for the Hardy-Littlewood maximal operator
A general version of delta theorem
A generalisation of Mahler measure and its application in algebraic dynamical systems
We prove a generalisation of the entropy formula for certain algebraic -actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.
A generalised conical density theorem for unrectifiable sets.
A generalization of component categories
A Generalization of Folner's Condition.
A Generalization Of Fubini's Theorem For Banach Algebra-Valued Measures.
A generalization of Rademacher's theorem on complete differential
A generalization of Steinhaus' theorem to coordinatewise measure preserving binary transformations
A generalization of the individual ergodic theorem
A generalization of the Lagrange mean value theorem to the case of vector-valued mappings.
A generalization of the mean ergodic theorem
A generalization of the Nikodym boundedness theorem.
In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.
A Generalization of the Strict Topology.
A generalization of the Vitali covering theorem
A generalization of Yano's extrapolation theorem
A generalized dual maximizer for the Monge–Kantorovich transport problem
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.
A generalized dual maximizer for the Monge–Kantorovich transport problem∗
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic...
A generalized formula of Hardy.
A generalized Pettis measurability criterion and integration of vector functions
For Banach-space-valued functions, the concepts of 𝒫-measurability, λ-measurability and m-measurability are defined, where 𝒫 is a δ-ring of subsets of a nonvoid set T, λ is a σ-subadditive submeasure on σ(𝒫) and m is an operator-valued measure on 𝒫. Various characterizations are given for 𝒫-measurable (resp. λ-measurable, m-measurable) vector functions on T. Using them and other auxiliary results proved here, the basic theorems of [6] are rigorously established.