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This paper focuses on the H∞ filtering problem for a class of discrete-time systems with stochastic incomplete measurement and mixed random delays. A more realistic and accurate measurement mode is proposed to compensate for the negative influence of both missing data and different time delays in a random way. In the system, all of the stochastic variables are mutually independent but satisfy the Bernoulli binary distribution. In particular, the stochastic infinite distributed delays are introduced in the discrete-time domain. Sufficient conditions for the existence of the admissible filter are derived in terms of linear matrix inequalities, which ensures the asymptotic stability as well as a prescribed H∞ performance for the filter errors. A simulation example is exploited to demonstrate the effectiveness of the proposed design procedures.