The hydrodynamics that develops during the infall of the core of a massive star at the end of its hydrostatic evolutionary epoch can have a profound effect on its subsequent dynamical history. In this paper the important processes governing the infall hydrodynamics are explored both semi-analytically and numerically with the aim of explaining the results of large-scale numerical calculations. We focus in particular on the factors responsible for reducing the mass of the inner core. These factors are found to be mainly associated with general relativistic effects and with the production, equilibration, and transport ofv e 's. Semi-leptonicv e emission and absorption are responsible for virtually all of thev e production. They dominate the energy transfer rate between matter andv e 's, but, with the rates being skewed to high energy, they are an importantv e -matter equilibrator only for the high-energy tail of thev e distribution. Neutrinoelectron scattering (NES) plays the dominant role inv e -matter equilibration with the important result that the equilibration is nearly complete by trapping. A careful examination of conditions where the onset of neutrino trapping is occurring indicates that the trapping density is a function of the enclosed mass, increasing with decreasing distance from the core center, and increasing with the extent of thev e -matter equilibration. Though not the dominant contributor to thev e -matter energy transfer rate, NES dominates the matter entropy production rate with another important result that the electron capture rate on free protons is significantly increased before trapping. The result of all of this is a greatly reduced inner core mass by the time of core turn-around. For numerical calculations employing the LLPR equation of state (or something similar), and for precollapse models having iron cores as small as 1.35M ⊙ (the smallest used by the author), this reduction of the inner core mass leads to the generation of a weak shock which fails to eject mass in a promptffashion. The effect of the small inner core mass on the subsequent dynamical history of the core is unknown.