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Serverless computing has emerged as a very popular cloud technology, together with its companion Function-as-a-Service (FaaS) programming model enabling invocations of stateless functions from clients. An evolution of serverless is now taking place, shifting it towards the edge of the network and broadening its scope to stateful functions, as well. In this paper we argue that stateless vs. stateful is not a dichotomy of the application per se, but rather a time-varying property of most (if not all) applications, as confirmed by the analysis of real traces collected in a production environment. Based on this observation, we propose a mathematical formulation of a resource allocation problem that jointly encompasses both operation modes, dubbed lambda vs. mu, which can be solved efficiently at run-time by an edge orchestrator. We evaluate the proposed solution via simulation experiments in realistic network and workload conditions, which leads the way to the practical realization of a system where applications can freely adapt their current operation mode and optimize their performance at a minimum cost of operation from the network's perspective.