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In this paper, we utilize stochastic geometry to analyze the primary service (PS) outage performance for spectrum sharing in Rayleigh fading environment. Using this approach, the impacts of the secondary service (SS) parameters and wireless environment on the PS outage probability are analyzed. We further obtain a closed form for the PS outage probability. The maximum SS transmitter node density for a given outage probability constraint of the PS is then obtained. We also investigate the impact of secondary spectrum sensing on the PS outage probability. A novel approach is further proposed that provides tight approximation for the PS outage probability. The results of the proposed approach are then validated through analysis and simulations. We then consider power control in the secondary network and show that the truncated channel inversion power control significantly decreases the PS outage probability. Cases with centralized and decentralized cooperative spectrum sensing are also studied, and their corresponding PS outage probabilities are analyzed. Mean spatial throughput of the SS is also analyzed. We further investigate the impact of the PS outage constraint on the spatial throughput of the SS. Extensive simulations confirm our analytical derivations.