In many scientific and data-driven applications, machine learning models are increasingly used as measurement instruments, rather than merely as predictors of predefined labels. When the measurement function is learned from data, the mapping from observations to quantities is determined implicitly by the training distribution and inductive biases, allowing multiple inequivalent mappings to satisfy standard predictive evaluation criteria. We formalize learned measurement functions as a distinct focus of evaluation and introduce measurement stability, a property capturing invariance of the measured quantity across admissible realizations of the learning process and across contexts. We show that standard evaluation criteria in machine learning, including generalization error, calibration, and robustness, do not guarantee measurement stability. Through a real-world case study, we show that models with comparable predictive performance can implement systematically inequivalent measurement functions, with distribution shift providing a concrete illustration of this failure. Taken together, our results highlight a limitation of existing evaluation frameworks in settings where learned model outputs are identified as measurements, motivating the need for an additional evaluative dimension.