The set "X" will be non-measurable for any countably additive probability measure on "S": if "X" has zero measure, countable additivity would imply that the whole circle has zero measure.
Namely, if "X" has zero measure, countable additivity would imply that the whole circle has zero measure. The set "X" will be non-measurable if the measure is assumed to be a countably additive probability measure.
The set "X" will be non-measurable if the measure is assumed to be a countably additive probability measure. Namely, if "X" has zero measure, countable additivity would imply that the whole circle has zero measure.
The set "X" will be non-measurable if the measure is assumed to be a countably additive probability measure. Namely, if "X" has zero measure, countable additivity would imply that the whole circle has zero measure.