A method for measuring seismicity rate changes caused by the occurrence of major earthquakes in the surrounding crust is proposed. It is based on a nonstationary Poisson modeling of earthquake activity. An estimate of the seismicity rate change and a probability measure of seismicity triggering following a large shock are derived, and the removal of the influence of independent aftershock sequences of other nearby, previous earthquakes is attempted, without using more traditional declustering techniques. The seismicity rate change estimator is corrected for its natural bias in favor of positive changes, at short timescales, that has so far strongly hindered measures of seismicity quiescences. Three Californian earthquakes are examined using this method: the 1989 M7.1 Loma Prieta, the 1992 M7.3 Landers, and the 1994 M6.7 Northridge earthquakes. Positive triggering is very commonly observed, as expected, but quiescence is, however, more seldomly obtained, for timescales up to 100 days after the main shock. This relative absence of quiescence, as compared to typical predictions of Coulomb modeling, for example, is also independently observed through direct correlation analyses of Californian seismicity. The possibility that the stresses caused by the main shock are spatially highly variable may explain these observations.