Let f be an integrable function on an infinite measure space (S,S , π). We show that if a regenerative sequence {Xn}n≥0 with canonical measure π could be generated then a consistent estimator of λ ≡ ∫ S fdπ can be produced. We further show that under appropriate second moment conditions, a confidence interval for λ can also be derived. This is illustrated with estimating countable sums and inte...