Internal laws of probability, generalized likelihoods and Lewis' infinitesimal chances-A response to Adam Elga

Herzberg F. Internal laws of probability, generalized likelihoods and Lewis' infinitesimal chances-A response to Adam Elga. The British Journal for the Philosophy of Science. 2007;58(1):25-43

On Core-Walras Equivalence in Banach Spaces when Feasibility is defined by the Pettis Integral

The paper studies the core-Walras equivalence problem in the commodity space framework of Banach spaces, allocations being defined as Pettis integrable functions. In particular, a core-Walras equivalence result for a certain class of commodity spaces is established, without requiring that the commodity space be separable. on the other hand, responding to objections made against some recent core-Walras nonequivalence results in the Bochner integrable allocations setting, it is shown that these latter results carry over to the pettis integrable allocations setting, unless additional restrictions on the heterogeneity of agents´ preferences are in force.

The one-way Fubini property and conditional independence : an equivalence result

A process defined by a continuum of random variables with non-degenerate idiosyncratic risk is not jointly measurable with respect to the usual product σ-algebra. We show that the process is jointly measurable in a one-way Fubini extension of the product space if and only if there is a countably generated σ-algebra given which the random variables are essentially pairwise conditionally independent, while their conditional distributions also satisfy a suitable joint measurability condition. Applications include: (i) new characterizations of essential pairwise independence and essential pairwise exchangeability; (ii) when a one-way Fubini extension exists, the need for the sample space to be saturated if there is an essentially random regular conditional distribution with respect to the usual product σ-algebra