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N Sahebdjahromi - One of the best experts on this subject based on the ideXlab platform.

  • an extension result for continuous valuations
    Journal of The London Mathematical Society-second Series, 2000
    Co-Authors: Maurizio Alvarezmanilla, Abbas Edalat, N Sahebdjahromi
    Abstract:

    It is shown, by a simple and direct proof, that if a bounded valuation on a monotone convergence space is the supremum of a directed family of simple valuations, then it has a unique extension to a Borel measure. In particular, this holds for any directed complete partial order with the Scott topology. It follows that every bounded and continuous valuation on a continuous directed complete partial order can be extended uniquely to a Borel measure. The last result also holds for σ-finite valuations, but fails for directed complete partial orders in general.

  • an extension result for continuous valuations
    Electronic Notes in Theoretical Computer Science, 1998
    Co-Authors: Maurizio Alvarezmanilla, Abbas Edalat, N Sahebdjahromi
    Abstract:

    Abstract We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel σ-algebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The result also holds for σ-finite valuations, but fails for dcpo's in general.

Maurizio Alvarezmanilla - One of the best experts on this subject based on the ideXlab platform.

  • an extension result for continuous valuations
    Journal of The London Mathematical Society-second Series, 2000
    Co-Authors: Maurizio Alvarezmanilla, Abbas Edalat, N Sahebdjahromi
    Abstract:

    It is shown, by a simple and direct proof, that if a bounded valuation on a monotone convergence space is the supremum of a directed family of simple valuations, then it has a unique extension to a Borel measure. In particular, this holds for any directed complete partial order with the Scott topology. It follows that every bounded and continuous valuation on a continuous directed complete partial order can be extended uniquely to a Borel measure. The last result also holds for σ-finite valuations, but fails for directed complete partial orders in general.

  • an extension result for continuous valuations
    Electronic Notes in Theoretical Computer Science, 1998
    Co-Authors: Maurizio Alvarezmanilla, Abbas Edalat, N Sahebdjahromi
    Abstract:

    Abstract We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel σ-algebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The result also holds for σ-finite valuations, but fails for dcpo's in general.

Carolyn L. Talcott - One of the best experts on this subject based on the ideXlab platform.

  • From Operational Semantics to Domain Theory
    Information and Computation, 1996
    Co-Authors: Ian A. Mason, Scott F. Smith, Carolyn L. Talcott
    Abstract:

    AbstractThis paper builds domain theoretic concepts upon an operational foundation. The basic operational theory consists of a single step reduction system from which an operational ordering and equivalence on programs are defined. The theory is then extended to include concepts from domain theory, including the notions of directed set, least upper bound, complete partial order, monotonicity, continuity, finite element,ω-algebraicity, full abstraction, and least fixed point properties. We conclude by using these concepts to construct a (strongly) fully abstract continuous model for our language. In addition we generalize a result of Milner and prove the uniqueness of such models

Abbas Edalat - One of the best experts on this subject based on the ideXlab platform.

  • an extension result for continuous valuations
    Journal of The London Mathematical Society-second Series, 2000
    Co-Authors: Maurizio Alvarezmanilla, Abbas Edalat, N Sahebdjahromi
    Abstract:

    It is shown, by a simple and direct proof, that if a bounded valuation on a monotone convergence space is the supremum of a directed family of simple valuations, then it has a unique extension to a Borel measure. In particular, this holds for any directed complete partial order with the Scott topology. It follows that every bounded and continuous valuation on a continuous directed complete partial order can be extended uniquely to a Borel measure. The last result also holds for σ-finite valuations, but fails for directed complete partial orders in general.

  • an extension result for continuous valuations
    Electronic Notes in Theoretical Computer Science, 1998
    Co-Authors: Maurizio Alvarezmanilla, Abbas Edalat, N Sahebdjahromi
    Abstract:

    Abstract We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel σ-algebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The result also holds for σ-finite valuations, but fails for dcpo's in general.

Ian A. Mason - One of the best experts on this subject based on the ideXlab platform.

  • From Operational Semantics to Domain Theory
    Information and Computation, 1996
    Co-Authors: Ian A. Mason, Scott F. Smith, Carolyn L. Talcott
    Abstract:

    AbstractThis paper builds domain theoretic concepts upon an operational foundation. The basic operational theory consists of a single step reduction system from which an operational ordering and equivalence on programs are defined. The theory is then extended to include concepts from domain theory, including the notions of directed set, least upper bound, complete partial order, monotonicity, continuity, finite element,ω-algebraicity, full abstraction, and least fixed point properties. We conclude by using these concepts to construct a (strongly) fully abstract continuous model for our language. In addition we generalize a result of Milner and prove the uniqueness of such models