Insertion of a measurable function

Insertion of a gamma-continuous function

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

A New Fuzzy Measurable Function

This paper focuses on fuzzy measurable functions based on gradual numbers. Firstly, some new concepts about gradual numbers are introduced as preparation. And then, the concept of gradual numbervalued measurable functions is introduced and some of its properties are investigated. Mathematics Subject Classification: 03E72, 28E10

Integral of Measurable Function

One can prove the following propositions: (1) For all extended real numbers x, y holds |x− y| = |y − x|. (2) For all extended real numbers x, y holds y − x ≤ |x− y|. (3) Let x, y be extended real numbers and e be a real number. Suppose |x − y| < e and x 6= +∞ or y 6= +∞ but x 6= −∞ or y 6= −∞. Then x 6= +∞ and x 6= −∞ and y 6= +∞ and y 6= −∞. (4) For all extended real numbers x, y such that for...

Insertion of a Function Belonging to a Certain Subclass of R^x

insertion of a gamma-continuous function

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.