We consider a classical electrodynamic theory, in which the operational paradigm of Elementary Measurement implies that particles and fields are interdependent degrees of freedom in an action principle associated with the "elementary measurement", and are not elementary in themselves. In this model Maxwell's equations, with an empirically chosen Green function, are identities associated with each charged particie current in the elementary interaction. Making the action stationary with respect to the interacting degrees of freedom gives the equations of motion of the measurement. These are shown to be equivalent to those of the "Action-at-a-Distance" electrodynamics of Wheeler and Feynman, with the distinct advantage that no "complete absorber" assumption is ever needed. The difficulties associated with infinite self-energies and mass renormalization are absent from this theory and a consistent set of energy-momentum and angularmomentum conservation laws follows from the associated energy-momentum tensor. The mechanism of "measurement" radiation is discussed and is shown to predict similar results as that of Maxwell-Lorentz electrodynamics.