Abstract

Chance theory is a mathematical methodology for dealing with indeterminacy phenomena involving uncertainty and randomness. In this paper, some properties of chance space are investigated. Based on this, the subadditivity theorem, null-additivity theorem, and asymptotic theorem of chance measure are proved.

Highlights

  • Uncertainty theory founded by Liu [1] in 2007 is a branch of axiomatic mathematics based on normality, duality, subadditivity, and product axioms

  • A useful formula was presented by Liu and Ha [5] to calculate the expected values of monotone functions of uncertain variables

  • Dai and Chen [6] verified the positive linearity of entropy and presented some formulas for calculating the entropy of monotone function of uncertain variables

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Summary

Introduction

Uncertainty theory founded by Liu [1] in 2007 is a branch of axiomatic mathematics based on normality, duality, subadditivity, and product axioms. Liu [1] presented the concept of uncertain variable and uncertainty distribution. A measure inversion theorem was proposed by Liu [3] from which the uncertain measures of some events can be calculated via the uncertainty distribution. After proposing the concept of independence [4], Liu [3] presented the operational law of uncertain variables.

Results
Conclusion

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