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The measurement of the average received power is essential for power control and dynamic channel allocation in wireless communication systems. However, due to the effects of multipath fading and additive noise inherent to the wireless channel, there can be significant errors in such measurements. In this paper, the error statistics for average power measurements are considered; in particular, the probability distribution of the value of the average received power at the time of interest conditioned on an outdated measurement is obtained. The resulting expression should have high utility in the analysis of wireless communication systems. However, in this paper, the design of power control algorithms that minimize the average transmitted power required to achieve a desired outage probability for the link is considered. A number of novel power control algorithms based on various models for the error in the average power measurement are derived. Numerical results indicate that power control algorithms based on the accurate expression derived in this paper can demonstrate significant gains over those based on previous approximate models.