Several update rules for non-additive probabilities, among them the Dempster-Shafer rule for belief functions and certain update rules in the spirit of Bayesian statistics with multiple prior probabilities, are reviewed, investigated and compared with each other. This is done within the unifying framework of general, nonadditive measure and integration theory. The methods exposed here are capable of generalizing conditional expectation of random variables to the submodular or supermodular case at least if the given algebra is finite.