The size of nuclei in histological preparations from excised breast tumors is predictive of patient outcome (large nuclei indicate poor outcome). Pathologists take into account nuclear size when performing breast cancer grading. In addition,the mean nuclear area (MNA) has been shown to have independent prognostic value. The straightforward approach to measuring nuclear size is by performing nuclei segmentation. We hypothesize that given an image of a tumor region with known nuclei locations,the area of the individual nuclei and region statistics such as the MNA can be reliably computed directly from the image data by employing a machine learning model,without the intermediate step of nuclei segmentation. Towards this goal,we train a deep convolutional neural network model that is applied locally at each nucleus location,and can reliably measure the area of the individual nuclei and the MNA. Furthermore,we show how such an approach can be extended to perform combined nuclei detection and measurement,which is reminiscent of granulometry.