In this paper, Lebesgue decomposition type theorems for non-additive measure are shown under the conditions of null-additivity, converse null-additivity, weak null-additivity and σ-null-additivity, etc.. In our discussion, the monotone continuity of set function is not required.

The trichromatic system of measurement. although suitable for fields subtending around 2 . does not give a linear metric with larger fields because of the presence of rod receptors. Their presence is allowed for in the tetrachromatic colour match and so one might expect the tetracllromatic system to be more linear. it is the purpose of this paper to test this by compariq tetra~hromatie and tric...

Additivity plays a key role in program analysis. It is the basis for designing Galois connection based abstract interpretations, it makes a Data-Flow Analysis (DFA) problem easy being convertible into a Kildall’s general form, and provides a lattice-theoretic model for disjunctive analysis. In this paper we consider reversible transformers respectively making any monotone function additive and ...

BACKGROUND It is an inherent assumption in randomised controlled trials that the drug effect can be estimated by subtracting the response during placebo from the response during active drug treatment. OBJECTIVE To test the assumption of additivity. The primary hypothesis was that the total treatment effect is smaller than the sum of the drug effect and the placebo effect. The secondary hypoth...

A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifolds with boundary. Wall showed that this property is not true of signatures on...

We show that it is consistent relative to a weakly compact cardinal strong homology additive and compactly supported within the class of locally separable metric spaces. This complements work Mardešić Prasolov [14] showing Continuum Hypothesis implies countable sum Hawaiian earrings witnesses failure possess either these properties. Our results build directly on Lambie-Hanson second author [3] ...

BACKGROUND Pyrethroid insecticides bind to voltage-gated sodium channels and modify their gating kinetics, thereby disrupting neuronal function. Although previous work has tested the additivity of pyrethroids in vivo, this has not been assessed directly at the primary molecular target using a functional measure. OBJECTIVES We investigated the potency and efficacy of 11 structurally diverse fo...

As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity of the form x+qy = x+y+(1−q)xy is a characteristic property of Tsallis entropy. Rényi in [1] generalized Shannon entropy by means of Kolmogorov-Nagumo averages, by imposing additivity as a constraint. In this paper we show that there exists no generalization for Tsallis entropy, b...

We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entang...

We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entang...