Working within eDrawings Professional
Measuring within SOLIDWORKS files and eDrawings files exported from SOLIDWORKS Standard is possible. The enable measure option must be turned on, and is accessible via the Options button when using the File > Save As command to save an eDrawing file from SOLIDWORKS. There is also an enable measure option in eDrawings Pro that can be found near the bottom of the Save As window.
Working within the eDrawings Viewer (eDrawings Standard)
It is not possible to measure within SOLIDWORKS files. Moreover, the eDrawings Viewer cannot measure eDrawing files exported from SOLIDWORKS Standard, even if the enable measure option has been turned on. However, the eDrawings Viewer can measure eDrawing files exported from SOLIDWORKS Professional or Premium, provided the enable measure option has been turned on.
SOLIDWORKS Standard and eDrawings Pro on the Same Computer
When saving SOLIDWORKS files as eDrawing files (.eprt, .easm, or .edrw) from SOLIDWORKS Standard, SOLIDWORKS will perform a check to see if eDrawings Professional has been installed on the same machine. If it passes the check, the file will be saved out of SOLIDWORKS as if it were saved from eDrawings Professional. It will be review-enabled, allowing mark-up and (optionally) measure.
Original material relating to this topic can be found in the SOLIDWORKS Customer Portal Knowledge Base, solution articles S-037765 & S-046922.
Anybody can download the eDrawings viewer. Seats of eDrawings Professional can be purchased as standalone or network licenses.