Existing methods for open set action recognition focus on novelty detection that assumes video clips show a single action, which is unrealistic in the real world. We propose a new method for open set action recognition and novelty detection via MUlti-Label Evidential learning (MULE), that goes beyond previous novel action detection methods by addressing the more general problems of single or multiple actors in the same scene, with simultaneous action(s) by any actor. Our Beta Evidential Neural Network estimates multi-action uncertainty with Beta densities based on actor-context-object relation representations. An evidence debiasing constraint is added to the objective func- tion for optimization to reduce the static bias of video representations, which can incorrectly correlate predictions and static cues. We develop a primal-dual average scheme update-based learning algorithm to optimize the proposed problem and provide corresponding theoretical analysis. Besides, uncertainty and belief-based novelty estimation mechanisms are formulated to detect novel actions. Extensive experiments on two real-world video datasets show that our proposed approach achieves promising performance in single/multi-actor, single/multi-action settings. Our code and models are released at https://github.com/charliezhaoyinpeng/mule.