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We study the coverage properties of large-scale sensor networks. Three coverage measures are defined to characterize the fraction of the area covered by sensors (area coverage), the fraction of sensors that can be removed without reducing the covered area (node coverage), and the capability of the sensor network to detect objects moving in the network (detectability), respectively. We approach the coverage problem from a theoretical perspective and explore the fundamental limits of the coverage of a large-scale sensor network. We characterize the asymptotic behavior of the coverage measures for a variety of sensor network scenarios. We find that the coverage of a sensor network exhibits different behaviors for different network configuration and parameters. Based on the analytical characterizations of the network coverage, we further discuss the implications to network planning and protocol performance of sensor networks.