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This paper considers a wireless powered multiuser mobile edge computing (MEC) system, in which a multi-antenna hybrid access point (AP) wirelessly charges multiple users, and each user relies on the harvested energy to execute computation tasks. We jointly optimize the energy beamforming and remote task execution at the AP, as well as the local computing and task offloading, aiming to minimize the total system energy consumption over a finite time horizon, subject to causality constraints for both energy harvesting and task arrival at the users. In particular, we consider a practical scenario with casual task state information (TSI) and channel state information (CSI), i.e., only the current and previous TSI and CSI are available, but the future TSI and CSI can only be predicted subject to certain errors. To solve this real-time resource allocation problem, we propose an offline-optimization inspired online design approach. First, we consider the offline optimization case by assuming that the TSI and CSI are perfectly known a-priori. In this case, the energy minimization problem corresponds to a convex problem, for which the semi-closed-form optimal solution is obtained via the Lagrange duality method. Next, inspired by the optimal offline solution, we propose a sliding-window based online resource allocation design in practical cases by integrating with the sequential optimization. Finally, numerical results show that the proposed joint wireless powered MEC designs significantly improve the system's energy efficiency, as compared with the benchmark schemes that consider a sliding window of size one or without such joint optimization.