We present models that offer coherent upper conditional predictions for both bounded and unbounded random variables within a metric space. These models are built upon various dimensional outer measures, and we explore the relationships between them. Specifically, we consider lower and upper Hewitt-Stromberg s-dimensional outer measures, packing outer measures, centered Hausdorff outer measures, and other types of outer measures. By employing a dimensional outer measure, even in cases where the metric space lacks second countability, we can determine whether the conditioning event has a zero, positive, finite, or infinite dimensional outer measure in its respective dimension. When the conditioning event possesses a positive and finite-dimensional outer measure in its dimension, we define the coherent upper conditional prevision using the Choquet integral. Furthermore, this prevision adheres to an extended version of the Monotone Convergence Theorem for non-linear integrals. This property ensures the equivalence between unbounded random variables that share the same distribution. Conversely, if the conditioning event has a dimensional outer measure of zero or infinity, the coherent upper conditional prevision is defined based on a finitely additive probability that takes 0–1 values and is not countably additive. The versatility of this model allows for making inferences whenever partial information is represented by fractal structures, as fractals can effectively capture the complexity of the given information.