The distance - based regularity measure of mining area is an index to evaluate the continuum and regularity of a mining area in an open pit. If it is added to a general open pit mine production scheduling model, a more practical plan of production scheduling of a open pit can be achieved. This paper proofs by theorems that the regularity measure of mining area has three attributes, i. e., square - first, translatability and rotatability, as such its rationality is verified from another view and the mathe- matical foundation for further application is laid.