If a sequence of measurable mappings defined from a measure spaces to another measure space converges in different modes (see Wikipedia and John Cook's site), I wonder if there are some concepts capturing their rates of convergence for different modes of convergence?
You may restrict the discussion to probability theory. One example is in statistics. Suppose $\theta_n$ is an estimator for $\theta^*$ based on a sample with sample size $n$. I was wondering how the rate of convergence of $\theta_n$ is defined?
I also appreciate if there can be some references offered.
Thanks and regards!