Properties of Caratheodor ’ s Measure

The paper contains definitions and basic properties of Caratheodor’s measure, with values inR, the enlarged set of real numbers, where R denotes set R = R ∪ {−∞,+∞} by [10]. The article includes the text being a continuation of the paper [5]. Caratheodor’s theorem and some theorems concerning basic properties of Caratheodor’s measure are proved. The work is the sixth part of the series of articles concerning the Lebesgue measure theory.