Keywords: Monotone measure Atom Weak null-additivity Regularity Sugeno integral Choquet integral a b s t r a c t In this paper, we prove some properties of atoms of weakly null-additive monotone measures. By using the regularity and weak null-additivity, a sin-gleton characterization of atoms of monotone measures on a metric space is shown. It is a generalization of previous results obtained by...

A natural generalization of (classical) measures are monotone set valued functions, the so called non-additive measures. Further generalization of measures are intervalvalued measures and interval-valued non-additive measures. Since interval-valued ⊕-measures, as a special case of intervalvalued non-additive measures, have been extensively applied in the mathematical representation of the vario...

Nonadditive measure is a generalization of additive probability measure. Sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. Integral inequalities play important roles in classical probability and measure theory. The classical Berwald integral inequality is one of the famous inequalities. This inequality turns out to have ...

In the present communication a generalized cost measure of utilities and lengths of output codewords from a memoryless source are defined. Lower and upper bounds in terms of a non-additive generalized measure of ‘useful’ information are obtained.

This paper is a brief summary of “M.Takahashi, T.Murofushi, S.Asahina, A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory, Fuzzy Sets and Systems, to appear.” This paper states that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary an...

The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion ofthe theory ofinner measures, their construction, and the relationship oftheir prop...