SSAS: T-SQL Equivalent for a Many-to-Many relationship

This question came a while ago now in this SSAS forum thread: What is wrong in my query and I thought it was something that may interest other people.

Basically it boiled down to trying to find a T-SQL equivalent to the following MDX which is querying a dimension with a many-to-many relationship to the measure.

So given the following simple MDX query, what would be the equivalent in SQL?