scholarly journals Set-Operational Properties of Semiatoms in Non-additive Measure Theory

2001 ◽  
Vol 263 (2) ◽  
pp. 637-654 ◽  
Author(s):  
Toshiaki Murofushi ◽  
Katsushige Fujimoto
Keyword(s):  
Measure Theory ◽  
Additive Measure

scholarly journals Premium Calculation by Transforming the Layer Premium Density

1996 ◽  
Vol 26 (1) ◽  
pp. 71-92 ◽  
Author(s):  
Shaun Wang
Keyword(s):  
Distribution Function ◽  
Decision Theory ◽  
Stochastic Dominance ◽  
Measure Theory ◽  
Additive Measure ◽  
Proportional Hazard ◽  
Economic Decision ◽  
Recent Developments ◽  
Premium Calculation ◽  
Economic Decision Theory

AbstractThis paper examines a class of premium functionals which are (i) comonotonic additive and (ii) stochastic dominance preservative. The representation for this class is a transformation of the decumulative distribution function. It has close connections with the recent developments in economic decision theory and non-additive measure theory. Among a few elementary members of this class, the proportional hazard transform seems to stand out as being most plausible for actuaries.

Lebesgue theorems in non-additive measure theory

2005 ◽  
Vol 149 (3) ◽  
pp. 543-548 ◽  
Author(s):  
Jinjie Song ◽  
Jun Li
Keyword(s):  
Measure Theory ◽  
Additive Measure

Conditions for Egoroff's theorem in non-additive measure theory

2004 ◽  
Vol 146 (1) ◽  
pp. 135-146 ◽  
Author(s):  
Toshiaki Murofushi ◽  
Kenta Uchino ◽  
Shin Asahina
Keyword(s):  
Measure Theory ◽  
Additive Measure

Relationship among continuity conditions and null-additivity conditions in non-additive measure theory

2006 ◽  
Vol 157 (5) ◽  
pp. 691-698 ◽  
Author(s):  
Shin Asahina ◽  
Kenta Uchino ◽  
Toshiaki Murofushi
Keyword(s):  
Measure Theory ◽  
Additive Measure

A Research on Text Classification Based on the Sugeno Integral

2014 ◽  
Vol 644-650 ◽  
pp. 1943-1946
Author(s):  
Shu Chao Feng ◽  
Wen Qian Shang
Keyword(s):  
Text Classification ◽  
Measure Theory ◽  
Frequency Theory ◽  
Fuzzy Measure ◽  
Occurrence Frequency ◽  
Additive Measure ◽  
Sugeno Integral ◽  
Measure Model ◽  
Weight Method

In this paper, we apply the Sugeno integral to text classification, which generalizes its usefulness as a classifier. In the classifier, the traditional weight method is replaced by fuzzy measure. Based on word co-occurrence frequency theory, which is improved in the paper, and based on 2-additive measure theory, this paper build a fuzzy measure model well. The paper creates the Sugeno integral text classifier in the last.

scholarly journals Quasi-pseudometric properties of the Nikodym-Saks space

2003 ◽  
Vol 4 (2) ◽  
pp. 243 ◽  
Author(s):  
Jesús Ferrer
Keyword(s):  
Functional Analysis ◽  
Metric Space ◽  
Measure Theory ◽  
Complete Metric Space ◽  
Additive Measure ◽  
Topological Properties ◽  
Pseudometric Space

<p>For a non-negative finite countably additive measure μ defined on the σ-field Σ of subsets of Ω, it is well known that a certain quotient of Σ can be turned into a complete metric space Σ (Ω), known as the Nikodym-Saks space, which yields such important results in Measure Theory and Functional Analysis as Vitali-Hahn-Saks and Nikodym's theorems. Here we study some topological properties of Σ (Ω) regarded as a quasi-pseudometric space.</p>

A METRIC ON SPACE OF MEASURABLE FUNCTIONS AND THE RELATED CONVERGENCE

2012 ◽  
Vol 20 (02) ◽  
pp. 211-222 ◽  
Author(s):  
GANG LI
Keyword(s):  
Measure Theory ◽  
Additive Measure ◽  
Convergence In Measure ◽  
Measurable Functions

A new metric is proposed on the space of measurable functions in the setting of non-additive measure theory. The convergence induced from the metric can be used to describe the convergence in measure for sequences of measurable functions. Furthermore, the space of measurable functions is complete under the metric.

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