A METRIC ON SPACE OF MEASURABLE FUNCTIONS AND THE RELATED CONVERGENCE

GANG LI

doi:10.1142/s0218488512500109

A METRIC ON SPACE OF MEASURABLE FUNCTIONS AND THE RELATED CONVERGENCE

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512500109 ◽

2012 ◽

Vol 20 (02) ◽

pp. 211-222 ◽

Cited By ~ 2

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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Lacunary ideal convergence in measure for sequences of fuzzy valued functions

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202624 ◽

2021 ◽

Vol 40 (3) ◽

pp. 5517-5526

Author(s):

Ömer Kişi

Keyword(s):

Measure Space ◽

Finite Measure ◽

Ideal Convergence ◽

Convergence In Measure ◽

Ideal Form ◽

Measurable Functions ◽

Finite Measure Space ◽

Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

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Premium Calculation by Transforming the Layer Premium Density

Astin Bulletin ◽

10.2143/ast.26.1.563234 ◽

1996 ◽

Vol 26 (1) ◽

pp. 71-92 ◽

Cited By ~ 391

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.

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

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.2001.7643 ◽

2001 ◽

Vol 263 (2) ◽

pp. 637-654 ◽

Cited By ~ 1

Author(s):

Toshiaki Murofushi ◽

Katsushige Fujimoto

Keyword(s):

Measure Theory ◽

Additive Measure

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Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

Journal of Mathematics ◽

10.1155/2021/6655630 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Ömer Kişi

Keyword(s):

Statistical Convergence ◽

Double Sequence ◽

Finite Measure ◽

Measurable Space ◽

Double Sequences ◽

Convergence In Measure ◽

Measurable Functions ◽

Lacunary Statistical Convergence ◽

Convergence Of Sequences ◽

Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

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