The above definition of mixing is meant to capture the intuitive notion of physical mixing. A canonical example is the Cuba libre : suppose one is adding rum (the set A ) to a glass of cola. After stirring the glass (the transformation T k for large k ), the bottom half of the glass (the set B ) will contain rum, and it will be in equal proportion as it is elsewhere in the glass. The mixing is uniform: no matter which region B one looks at, some of A will be in that region. The use of T − − k in the definition, instead of T k , is required because the time evolution transformation T is typically not an injective function (one-to-one). That is, if T maps two points into one, the measure is preserved only by counting the two points in the pre-image, instead of one point in the image.