A measure is a numerical property of a multidimensional cube, e.g., sales price, coupled with an aggregation formula, e.g., SUM. It captures numerical information to be used for aggregate computations.
As an example, a three-dimensional cube for capturing sales may have a Product dimension P, a Time dimension T, and a Store dimension S, capturing the product sold, the time of sale, and the store it was sold in, for each sale, respectively. The cube has two measures: DollarSales and ItemSales, capturing the sales price and the number of items sold, respectively. ItemSales can be viewed as a function: ItemSales: Dom(P) × Dom(T) × Dom(S) ↦ ℕ0 that given a certain combination of dimension values returns the total number of items sold for that combination. If a dimension value corresponds to a higher level in the dimension hierarchy, e.g., a product group or even all products, the result is an aggregation of several lower-level measure values ....
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