In this paper, we investigate the properties of the Dunford-Schwartz integral (the integral with respect to a finitely additive measure). Though it is not equivalent to the cylinder integral, we can show that a cylinder probability ν on (H, C) can be...
In this paper, we investigate the properties of the Dunford-Schwartz integral (the integral with respect to a finitely additive measure). Though it is not equivalent to the cylinder integral, we can show that a cylinder probability ν on (H, C) can be extend as a finitely additive probability measure ν^ on a field C^ ⊃ C which is equivalent to the Dunford-Schwartz integral on (H, C^, ν^).