OLAP Cube Review
Consider the 3-dimensional OLAP cube above. The three dimensions of the cube are "Product", "Geography", and "Time". "Sales Amount" is the measure being summarized, and is often considered an additional dimension of the cube. OLAP cubes can be N-dimensional, while this one has three dimensions.
Within each dimension are hierarchies, or ways of organizing the dimension into various levels of granularity. For example, within the Time dimension there can exist the Calendar Year / Quarter / Month / Day hierarchy. Likewise, the Time dimension can also have the Fiscal Year / Quarter / Month / Day hierarchy. Each of Year / Quarter / Month / Day represents levels in the hierarchy. '2003' is considered a member of the 'Year' level within the hierarchy. Likewise, the Product dimension can have multiple hierarchies. A hierarchy could be constructed based on the type of product while another hierarchy could be constructed based on the color of the product.
In the example above, picking a member from one dimension would be visualized as a slice through the cube. For example, picking '' from the Geography dimension could be a relatively thick slice of the cube, if there were many levels underneath 'Country', like 'State', 'City', and 'PostalCode'. Picking a member from Geography that is more granular than 'Australia" results in a thinner slice of the cube in the Geography dimension, because now some of will have been omitted from the data.
A tuple is the intersection of two or more members from distinct dimensions. In the example above, three members from three dimensions are expressed:
From Geography we have [Geography].[Country].&[Australia]
From Product we have [Product].[Cars].children
From Time we have [Time].[Calendar].[Calendar Year].&[2003]