  Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an
explanation for quantum probabilities. We show that the values given by the
Born rule equal projection factors, describing the contraction of Lebesgue
measures in orthogonal projections from the complex line of a quantum state to
eigenspaces of an observable. Unit total probability corresponds to a complex
Pythagorean theorem: the measure of a subset of the complex line is the sum of
the measures of its projections on all eigenspaces. To show that projection
factors can work as probabilities, we postulate the existence of a continuum
infinity of identical quantum universes, all with the same quasi-classical
worlds. In a measurement, these factors give the relative amounts of worlds
with each result, which we associate to frequentist and Bayesian probabilities.
This solves the probability problem of Everett's theory, allowing its preferred
basis problem to be solved as well, and may help settle questions about the
nature of probability.
