However, the equivalence assumption is important in the literature on asymmetric information (e.g. Amendinger et al. (1998,2003); Grorud and Pontier (1998)) since it ensures the existence of the decoupling measure (see Proposition 2.4) under which the information variable and the reference filtration are independent.
Thus, we can deduct the following proposition: Proposition 2 deduces under which conditions retail formats will be diverse.
We prove a proposition asserting conditions under which the robustness curves for two different designs will cross one another, entailing the potential for reversal of preference between the two designs.
end{aligned} (2.12) Before stipulating a criterion of self-adjointness, we give a proposition which states conditions under which (Zin D(A^)), quoted from [15], Proposition 10.3.3.
Coherence theorists can argue that the truth conditions of a proposition are the conditions under which speakers make a practice of asserting it.
Coherentists can argue that the only conditions speakers can recognise as justifying a proposition are the conditions under which it coheres with their beliefs.
Even though this objective fact obtains, the truth conditions of propositions, including propositions about which sets of propositions are believed, are the conditions under which they cohere with a set of propositions.
We employ case evidence from firms in the fields of foundation engineering, tunnel construction, tea-packaging, and geological surveying to derive a set of five propositions regarding the conditions under which user manufacturer diversification is attractive and viable in the long run.
In the next proposition, we give sufficient conditions under which (129) has a solution (omega_{k_{2}}^{d} tau,m,epsilon)) in the Banach space (F_{(nu',beta,mu,k_{2})}^{d}) where (nu'), β, μ are defined above.
end{aligned} (83) In the next proposition, we give sufficient conditions under which (83) has a solution (omega_{k_{1}}^{d} tau,m,epsilon)) in the Banach space (F_{(nu,beta,mu,k_{1},kappa)}^{d}) where β, μ are defined above and for well chosen (kappa> k_{1}).
