Abstract
The Born rule may be stated mathematically as the rule thatprobabilities in quantum theory are expectation values of a completeorthogonal set of projection operators. This rule works for singlelaboratory settings in which the observer can distinguish all thedifferent possible outcomes corresponding to the projection operators. However, theories of inflation suggest that the universe may be so largethat any laboratory, no matter how precisely it is defined by itsinternal state, may exist in a large number of very distantly separatedcopies throughout the vast universe. In this case, no observer withinthe universe can distinguish all possible outcomes for all copies of thelaboratory. Then normalized probabilities for the local outcomes thatcan be locally distinguished cannot be given by the expectation valuesof any projection operators. Thus the Born rule fails and must bereplaced by another rule for observational probabilities in cosmology. The freedom of what this new rule is to be is the measure problem incosmology. A particular volume-averaged form is proposed.
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