Spaces of Measures

Constantinescu, Corneliu

doi:10.1515/9783110853995

Cited by 10 publications

(18 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By Proposition 5.1.12 of Constantinescu (1984), there is a finite family of strictly positive and σ-finite measures (ν 51 Here, M σ (Ω, P(F)) is quipped with the natural ordering and the total variation norm.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Radner Equilibria Under Ambiguous Volatility

Beißner

2013

SSRN Journal

View full text Add to dashboard Cite

The present paper considers a class of general equilibrium economies when the primitive uncertainty model features uncertainty about continuous-time volatility. This requires a set of mutually singular priors, which do not share the same null sets. For this setting we introduce an appropriate commodity space and the dual of linear and continuous price systems. All agents in the economy are heterogeneous in their preference for uncertainty. Each utility functional is of variational type. The existence of equilibrium is approached by a generalized excess utility fixed point argument. Such Arrow-Debreu allocations can be implemented into a Radner economy with continuous-time trading. Effective completeness of the market spaces alters to an endogenous property. Only mean unambiguous claims equivalently satisfying the classical martingale representation property build the marketed space.

show abstract

Section: Proof Of Theoremmentioning

confidence: 99%

Radner Equilibria Under Ambiguous Volatility

Beißner

2013

SSRN Journal

View full text Add to dashboard Cite

show abstract

“…The properties of r~ are as follows: In what follows we shall use the terminology of topological Riesz spaces. For detailed information on Hausdorff locally convex-solid Riesz spaces, we refer to the book by Aliprantis and Burkinshaw [3]; Hausdorfflocally convex-solid Riesz spaces of type M are studied in the book by Constantinescu [ 13], where they are called M-spaces. The space H will be called the embedding space ofF and the map j: F --, H will be called the embedding map.…”

Section: The Class G Is a Riesz Space In Particular The Zero Elemenmentioning

confidence: 99%

Embedding theorems for classes of convex sets

Schmidt

1986

Acta Appl Math

View full text Add to dashboard Cite

R/idstrOm's embedding theorem states that the nonempty compact convex subsets of a normed vector space can be identified with points of another normed vector space such that the embedding map is additive, positively homogeneous, and isometric. In the present paper, extensions of R~dstr6m's embedding theorem are proven which provide additional information on the embedding space. These results include those of H6rmander who proved a similar embedding theorem for the nonempty closed bounded convex subsets ofa Hausdorfflocally convex vector space. In contrast to HOrmander's approach via support function als, all embedding theorems of the present paper are proven by a refinement of Rgtdstr6m's original method which is constructive and does not rely on Zorn's lemma. This paper also includes a brief discussion of some actual or potential applications of embedding theorems for classes of convex sets in probability theory, mathematical economics, interval mathematics, and related areas.

show abstract

“…There are few works about integration in a classical Banach space, that is over the field R of real numbers or the field C of complex numbers [5,6,7,8,38,42]. On the other hand, for a non-Archimedean Banach space X (that is over a non-Archimedean field) this theory is less developed.…”

Section: Introductionmentioning

confidence: 99%

“…W(F, W, V ; U) := {([µ], [ν]) ∈ Ω 2 |{B : ([µ], [ν])(B, g, x) ∈ U, g ∈ W, x ∈ V } ∈ F},where F is a filter on R (compare with § 2.1 and 4.1[7]);(4) W(A, G; U) := {([µ], [ν]) ∈ Ω 2 | {(g, x) : ([µ], [ν])(B, g, x) ∈ U, B ∈ A} ∈ G},…”

mentioning

confidence: 99%

“…such that ν(c, * ) are measures on Bf (V c ). Choosing V c ⊂ V c ′ for c > c ′ and defining ν(A) := lim c→+0 ν(c, A ∩ V c ) for each A ∈ Bf (X) in view of the Radon-Nikodym theorem about convergence of measures (see [7]) we get (i) with the help of the theorem about extension of measures, since the minimal σ-field σBco(X) generated by Bco(X) coincides with Bf (X). 4.5.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space

Lüdkovsky

2005

J Math Sci

View full text Add to dashboard Cite

Quasi-invariant and pseudo-differentiable measures on a Banach space X over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in R. Theorems and criteria are formulated and proved about quasi-invariance and pseudo-differentiability of measures relative to linear and non-linear operators on X. Characteristic functionals of measures are studied. Moreover, the non-Archimedean analogs of the Bochner-Kolmogorov and Minlos-Sazonov theorems are investigated. Infinite products of measures also are considered. Convergence of quasi-invariant and pseudo-differentiable measures in the corresponding spaces of measures is investigated.

show abstract

Spaces of Measures

Cited by 10 publications

References 0 publications

Radner Equilibria Under Ambiguous Volatility

Radner Equilibria Under Ambiguous Volatility

Embedding theorems for classes of convex sets

Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space

Contact Info

Product

Resources

About