A minimal P-complete extension of the sigma-algebra makes L^∞(P) the dual of the space of signed measures absolutely continuous w.r.t. at least one member of P.
Quasi-sure analysis, aggregation and dual representations of sublinear expec- tations in general spaces.Electronic Journal of Probability, 17(none):1 – 15, 2012
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Can the $L^1$-$L^\infty$ duality be restored for non-dominated families of probability measures?
A minimal P-complete extension of the sigma-algebra makes L^∞(P) the dual of the space of signed measures absolutely continuous w.r.t. at least one member of P.