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You can use MDX to specify a name for set expressions (named sets). You can also define formulas and treat each formula as a new member.
Named sets are useful because they can be used concisely in other MDX statements. Creating formulas and treating them as members of a dimension is a very powerful feature and has a variety of applications.
For an illustration of these concepts, see the following examples:
Defining a New Member Example shows how to define a new member on a dimension.
Defining and Qualifying a New Member Example shows how to define and qualify a new member for a specific dimension.
Assigning a Solve Order Example shows how to assign a solve order for calculated members.