I was going through the minimum variance unbiased estimators and I am confused about the concept of MVUE and UMVUE. Is the unbiased estimator whose variance attaining CRLB a UMVUE or MVUE? I referred two books. One of those(A first course on parametric inference by B.K.Kale ) says that the unbiased estimator attaining CRLB is MVUE and the other(An introduction to probability and statistics by Rohatgi) says that it is UMVUE. So, are they same?