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Based on the panel data of 31 provinces (municipalities and autonomous regions) in China from 2012 to 2019, this paper constructs the evaluation index system of basic medical and health services in China from seven dimensions: medical and health facilities, health expenditure, medical services, traditional Chinese medicine hospital services, maternal and child health care, people's health and medical security, disease control and public health. The entropy method was used to measure the level of basic medical and health services in China, and its spatial differences and convergence characteristics were further investigated. In this study, we employ the entropy weight method, σ convergence, and β convergence as our primary methodologies. The entropy weight method is used to evaluate the variability of each indicator, determine the weights of indicators, and quantify the information content of the data. σ convergence illustrates the process by which the variance of a sample decreases over time. β convergence refers to the gradual approach of variables within an economic system towards their long-term equilibrium level over time. The results show that: (1) The scores of basic medical and health services in China's four major regions (including Northeast, East, Central and West) remain in a relatively stable state, with small fluctuations and great room for improvement; (2) There are significant regional differences in the level of basic medical and health services in China, and the intra-regional differences are much greater than the inter-regional differences; (3) There is no significant σ convergence observed in China and its four major regions; however, there is a notable presence of β convergence. [ABSTRACT FROM AUTHOR]