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In wireless networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. A unified framework is introduced that permits the geometric characterization of fading by incorporating the fading process into the point process model. Concretely, assuming nodes are distributed in a stationary Poisson point process in Rd , the properties of the point processes that describe the path loss with fading are analyzed. The main applications are single-hop connectivity and broadcasting.