Measurability of functionals and of ideal point forecasts

The ideal probabilistic forecast for a random variable Y based on an information set F is the conditional distribution of given F. In context point forecasts aiming to specify functional T such as mean, quantile or risk measure, respective applied distribution. This paper provides theoretical justification why this actually forecast, that is, F-measurable variable. To end, appropriate notion measurability clarified and established large class practically relevant functionals, including elicitable ones. More generally, implies any which arises by applying forecast. Similar results are proper scoring rules, main tool evaluate predictive accuracy forecasts.