Bergmann Bounce Relativity in Multiverses: Resolving the Measure Problem through Stochastic Overlaps

The Measure Problem in multiverse theories, particularly Eternal Inflation, arises from the infinite number of bubble universes, rendering probabilistic predictions ill-defined. Bergmann Bounce Relativity (BBR) integrates stochastic mini-bounces into General Relativity, introducing a finite, stochastic measure via the bounce rate λ = σ n_γ² V / c. Overlapping bounces between bubble universes create connected multiverses, enabling information exchange and regularizing probabilities without anthropic selection or arbitrary cutoffs. This paper derives the bounce-overlap metric, analyzes stability in bubble collisions, compares with existing multiverse measures (volume weighting, comoving measure, geodesic measures), and provides quantitative, testable predictions including gravitational wave backgrounds at 10^{-16} Hz and CMB cold-spot anomalies. BBR/BMC offer a pathway to resolve the Measure Problem while unifying quantum gravity and cosmology.