Belief functions on real numbers

We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbersR = [−∞,∞], under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality functions become integrals of these densities and pignistic probabilities become pignistic densities. The mathematics of belief functions become essentially the mathematics of probability density functions on R.