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Automatically measuring lesion/tumor size with RECIST (Response Evaluation Criteria In Solid Tumors) diameters and segmentation is important for computer-aided diagnosis. Although it has been studied in recent years, there is still space to improve its accuracy and robustness, such as (1) enhancing features by incorporating rich contextual information while keeping a high spatial resolution and (2) involving new tasks and losses for joint optimization. To reach this goal, this paper proposes a transformer-based network (MeaFormer, Measurement transFormer) for lesion RECIST diameter prediction and segmentation (LRDPS). It is formulated as three correlative and complementary tasks: lesion segmentation, heatmap prediction, and keypoint regression. To the best of our knowledge, it is the first time to use keypoint regression for RECIST diameter prediction. MeaFormer can enhance high-resolution features by employing transformers to capture their long-range dependencies. Two consistency losses are introduced to explicitly build relationships among these tasks for better optimization. Experiments show that MeaFormer achieves the state-of-the-art performance of LRDPS on the large-scale DeepLesion dataset and produces promising results of two downstream clinic-relevant tasks, i.e., 3D lesion segmentation and RECIST assessment in longitudinal studies.