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Analytical approaches to problem solving consist of two steps: 1 Modeling the problem, 2 Solving the model. In stochastic programming (both in literature and in practice), modeling is often done only on a descriptive level where one never specifies the true model whose solution is sought. This is partly due to the fact that often all natural candidates for a true model are infinite-dimensional optimization problems involving mathematical concepts that practitioners are not always familiar with. Indeed, in many problems, there are essential (not just technical) features that can be captured only in terms of infinite-dimensional spaces. Such general stochastic programming models were well-developed already in the 1970's, but it seems that, as stochastic programming gained popularity among practitioners, they were partly forgotten. Nowadays, stochastic programming models of real-life problems are often formulated in terms of scenario trees constructed in an ad-hoc manner. This has resulted in vague formulations of stochastic programs that lack interpretation. Our aim is to describe an analytical version of the stochastic programming approach for practical decision making. In our approach, both the modeling and solution phases are broken down into two sub-phases: 1.1 Modeling the decision problem as an optimization problem, 1.2 Modeling the uncertainty, 2.1 Discretization of the optimization problem, 2.2 Numerical solution of the discretized problem. The first step consists of modeling the decision problem as a stochastic optimization problem over a general probability space. The second step consists of specifying the probability distribution of the uncertain data. The purpose of the third step is to construct finite-dimensional, numerically solvable, consistent approximations of the optimization model specified in the first two steps. The discretized model is then solved in the fourth step using appropriate techniques for stochastic programs over finite scenario trees. This kind of approaches to problem solving are familiar from other fields of applied mathematics such as ordinary or partial differential equations. Indeed, there also one models real phenomena by infinite-dimensional models, after which solutions are sought through discretization and numerical computation. Our approach has several advantages. First, it facilitates the solution process by decomposing it into more easily manageable pieces. Second, having a well-defined model allows for rigorous analysis of the problem and solution techniques. Third, it allows one to use well-developed models from various fields of stochastics where stochastic processes are not restricted to finite scenario trees. Fourth, this approach relates closely with other disciplines, making stochastic programming more attractive to a wider range of researchers and practitioners.