The vast majority of stochastic optimization problems require the approximation of the underlying probability measure, e.g., by sampling or using observations. It is therefore crucial to understand the dependence of the optimal value and optimal solutions on these approximations as the sample...

The main objective of this paper is a systematic representation of the basic theorems on line integrals to derive consistent and unique measures of welfare change. We describe the conditions of path independence, starting from the theoretical background of the Marshallian demand function, and...