Definition: Let A be a subset of $R^n $. We say A has measure zero in $ R^n $ if for every $\epsilon >0 $ , there is a covering $ Q_1,Q_2... $ of A by countably many rectangles such that $$\sum_{i=1}^{\infty} v(Q_i) <\epsilon $$. If this inequality holds, we often say that the total volume of the rectangles $ Q_1,Q_2... $ is less than $\epsilon $.
My question is is the measure 0 equivalent to say that the volume is 0?