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In this paper, we study resource allocation algorithm design for multiuser orthogonal frequency division multiple access (OFDMA) ultra-reliable low latency communication (URLLC) in mobile edge computing (MEC) systems. To achieve the stringent end-to-end delay and reliability requirements of URLLC MEC systems, we propose joint uplink-downlink resource allocation and finite blocklength transmission. Furthermore, we propose a partial time overlap between the uplink and downlink frames to minimize the end-to-end delay, which introduces new time causality constraints. Then, the proposed resource allocation algorithm is formulated as an optimization problem for minimization of the total weighted transmit power of the network under constraints on the minimum quality-of-service regarding the number of computed URLLC user bits within the maximum allowable computing time, i.e., the end-to-end delay of a computation task. Due to the non-convexity of the optimization problem, finding the globally optimal solution entails a high computational complexity which is not tolerable for real-time applications. Therefore, a low-complexity algorithm based on successive convex approximation is proposed to find a high-quality sub-optimal solution. Our simulation results show that the proposed resource allocation algorithm design facilitates the application of URLLC in MEC systems, and yields significant power savings compared to a benchmark scheme.