• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.17-25
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• 1999

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 v on (H, C) can be extend as a finitely additive probability measure $\hat{v}$ on a field $\hat{C}{\;}{\supset}{\;}C$ which is equivalent to the Dunford-Schwartz integral on ($H,{\;}\hat{C},{\;}\hat{v}$).