Beissner, PatrickDenis, Laurent2020-07-161945-497Xhttp://hdl.handle.net/1885/206289Any 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.application/pdfen-AU© 2018 Society for Industrial and Applied Mathematics (SIAM)asset pricinggeneral equilibrium under uncertaintyspace of contingent claimsvolatility uncertaintydual spacemutually singular probability measures2018-03-2710.1137/17M11208772020-04-05