According to the notation in [BuG01], the data cube in figure 1 can be stated here in the form given in [BuG01, page 222-223]:

In general a dimension D with m dimension values can be defined formally as a m tuple (a sorted list of m values):

Consequently, |D| = m defines the number of dimension values of the dimension D (cf. >Startseite >Informatik >Business Intelligence >Data Warehousing >>tab: Infos).

Furthermore, a (data) cube C can be specified in the following notation:

where:

• D_i represents the different dimensions,
• M_i : Typ_i describes the characteristic of the cube along with its data type

Based on this notation, the data cube in figure 1 can be generally defined as follows: