IDEAS home Printed from
   My bibliography  Save this paper

Convex radiant costarshaped sets and the least sublinear gauge


  • Alberto Zaffaroni



The paper studies convex radiant sets (i.e. containing the origin) of a linear normed space X and their representation by means of a gauge. By gauge of a convex radiant set C c X we mean a sublinear function p : X ==> R such that C = [p 0 : x e lC}, the set C may have other gauges, which are necessarily lower than mC. We characterize the class of convex radiant sets which admit a gauge different from mC in two different way: they are contained in a translate of their recession cone or, equivalently, they are costarshaped, that is complement of a starshaped set. We prove that the family of all sublinear gauges of a convex radiant set admits a least element and characterize its support set in terms of polar sets. The key concept for this study is the outer kernel of C, that is the kernel (in the sense of Starshaped Analysis) of the complement of C. We also devote some attention to the relation between costarshaped and hyperbolic convex sets.

Suggested Citation

  • Alberto Zaffaroni, 2012. "Convex radiant costarshaped sets and the least sublinear gauge," Center for Economic Research (RECent) 077, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
  • Handle: RePEc:mod:recent:077

    Download full text from publisher

    File URL:
    Download Restriction: no

    More about this item


    Convex sets; Minkowski gauge; sublinear gauge; radiant sets; costar-shaped sets; kernel; outer kernel; polar set; reverse polar; hyperbolic convex sets;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mod:recent:077. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.