During the descent of the Galileo probe through Jupiter's atmosphere, the lightning and radio emissions detector (LRD) instrument measured radio frequency signals presumably from electrical discharges in the planet's atmosphere. The LRD was the only instrument that provided remote sensing, as well as in situ, measurements of atmospheric characteristics. The LRD measurements are presented here and some estimates are given on the energetics and frequency of occurrence of lightning in Jovian clouds. Propagation calculations of RF discharges in the Jovian atmosphere system and the statistics data obtained by the LRD, together with one very distinct lightning waveform, permit a unified and consistent interpretation of the data. We conclude that at the time of probe entry, Jovian discharges occur with a rate about one hundredth that of the global yearly average on Earth (Earth value is about 6 flashes km⁻² yr⁻¹) within about 15,000 km radius of the probe and that the average radiated power is of the order of 5 × 10¹¹ W. The change in the electric dipole moment in Jovian lightning is about 10⁷ coulomb in, roughly 100 times that of a typical terrestrial discharge.