We have shown that the maximum achievable resolution of an in-line lensless holographic microscope is limited by aliasing and, for collimated illumination, cannot exceed the camera pixel size. This limit can be achieved only when the optimal conditions on the spatial and temporal coherence state of the illumination are satisfied. The expressions defining the configuration, delivering maximum resolution with given spatial and temporal coherence of the illumination, are obtained. The validity of these conditions is confirmed experimentally.