For the coin-flip process, the time-evolution operator formula_64 is the shift operator that says "throw away the first coin-flip, and keep the rest". Formally, if formula_65 is a sequence of coin-flips, then formula_66. The measure is obviously shift-invariant: as long as we are talking about some set formula_28 where the first coin-flip formula_68 is the "don't care" value, then the volume formula_7 does not change: formula_70. In order to avoid talking about the first coin-flip, it is easier to define formula_71 as inserting a "don't care" value into the first position: formula_72. With this definition, one obviously has that formula_73 with no constraints on formula_14. This is again an example of why formula_71 is used in the formal definitions.