Relationship among continuity conditions and null-additivity conditions in non-additive measure theory

The paper shows all the implication relationship among six continuity conditions and two null-additivity conditions with respect to non-additive measures. The six continuity conditions are continuity from above, order continuity, strong order continuity, exhaustivity, continuity from below, and null-continuity, and the two null-additivity conditions are null-additivity and weak null-additivity. The implication relationship is summarized in a diagram.