Topic
Subadditivity
About: Subadditivity is a research topic. Over the lifetime, 1116 publications have been published within this topic receiving 27615 citations.
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01 Jan 1994
TL;DR: In this article, the authors propose the integration of Monotone Functions on Intervals and the construction of measures using topology, based on the Radon-Nikodym Theorem.
Abstract: Preface. 1. Integration of Monotone Functions on Intervals. 2. Set Functions and Caratheodory Measurability. 3. Construction of Measures using Topology. 4. Distribution Functions, Measurability and Comonotonicity of Functions. 5. The Asymmetric Integral. 6. The Subadditivity Theorem. 7. The Symmetric Integral. 8. Sequences of Functions and Convergence Theorems. 9. Nullfunctions and the Lebesgue Spaces Lp. 10. Families of Measures and their Envelopes. 11. Densities and the Radon-Nikodym Theorem. 12. Products. 13. Representing Functionals as Integrals. References. Index.
1,327 citations
TL;DR: In this article, a two-step method was proposed to elicit individual preference functions and decision weights under rank-dependent expected utility theory and cumulative prospect theory. But the method is parameter-free and elicits the whole individual preference functional without imposing any prior restriction.
Abstract: This paper proposes a two-step method to successively elicit utility functions and decision weights under rank-dependent expected utility theory and its "more descriptive" version: cumulative prospect theory. The novelty of the method is that it is parameter-free, and thus elicits the whole individual preference functional without imposing any prior restriction. This method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains. Concave utility functions are obtained for gains and convex utility functions for losses. The elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations. The data also show that the probability weighting function for losses is more "elevated" than for gains.
934 citations
TL;DR: In this paper, it was shown that the quantum entropy is strongly subadditive, and several theorems about quantum-mechanical entropy were shown to hold for general entropy.
Abstract: We prove several theorems about quantum‐mechanical entropy, in particular, that it is strongly subadditive.
875 citations
TL;DR: A progress report on the last decade of subadditive stochastic processes can be found in this article, where Hammersley and Welsh discovered the first subaddive processes.
Abstract: It is now ten years since Hammersley and Welsh discovered (or invented) subadditive stochastic processes. Since then the theory has developed and deepened, new fields of application have been explored, and further challenging problems have arisen. This paper is a progress report on the last decade.
650 citations
TL;DR: Several convex mappings of linear operators on a Hilbert space into the real numbers were derived in this article, including the Wigner-Yanase-Dyson conjecture and the strong subadditivity of quantum mechanical entropy.
621 citations