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We consider a random variable Y and approximations Yn, n ∈ N, defined on the same probability space with values in the same measurable space as Y. We are interested in situations where the approximations Yn allow to define a Dirichlet form in the space L 2 (PY) where PY is the law of Y. Our approach consists in studying both biases and variances. The article attempts to propose a general theoretical framework. It is illustrated by severa