Replacing the G-continuity of F by ordered completeness of X yields the next theorem.
While ordering (completeness and transitivity) is important for the arguments below (as it is for substantial parts of economic theory), continuity is not.
For this process, individual data was first reduced to rank orderings, and then evaluated for three properties relevant for preference judgments, namely rank order "asymmetry", "completeness", and "transitivity" across conditions (defined below) [73].
Lippold's "Full Moon" (1949 50) and "Sun" (1953 56; commissioned by the Metropolitan Museum of Art, New York City, to hang in its room of Persian carpets) show an intuition of a basic regularity, precise order, and completeness that underlies the universe.
As the number of other cardiovascular or metabolic risk factors recorded in these participants varied, the results are presented in order of completeness of data.
The bridge principles must be explicitly added to the union of the original axiomatics in order to ensure completeness.
For example, in order to ensure completeness of the dataset in BDA, the data is to be retrieved from n sources: S1, S2, …, Sn.
Section 3 contains definitions and a discussion about the appropriate vector measures which we will need in order to get completeness of our Sobolev spaces with respect to measures.
On the other hand, if we adopt the order (1), the completeness data cleaning is firstly carried out, which will repair the lost data and is helpful to guarantee the performance of the secondary time-related data cleaning.
In order to ensure completeness and accuracy of data entry, two of the authors (SS, KM) independently entered the data into Microsoft Excel.
