Any dynamic or stochastic notion of a general equilibrium relies on the underlying commodity space. Under sole risk and without multiple--prior uncertainty the usual choice is a Lebesgue space from standard measure theory. In  the case of volatility uncertainty it turns out that such a type of function space is no longer appropriate. For this reason we introduce and discuss a new natural commodity space, which can be constructed in three independent and equivalent ways. Each approach departs from one possible way to construct Lebesgue spaces. Moreover, we give a complete representation of the resulting  topological dual space. This extends the classic Riesz representation in a natural way. Elements therein are the candidates for a linear equilibrium  price system.  This representation result has direct implications  for the microeconomic foundation of finance under Knightian uncertainty.

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