IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-29046-1_9.html
   My bibliography  Save this book chapter

The L p spaces

In: Measure and Integration

Author

Listed:
  • Hari Bercovici

    (Indiana University, Department of Mathematics)

  • Arlen Brown

    (Indiana University, Department of Mathematics)

  • Carl Pearcy

    (Texas A&M University, Department of Mathematics)

Abstract

So far in this book we have considered only pointwise, or almost everywhere, convergence of sequences (and nets) of measurable functions. In many problems where Lebesgue integration occurs, several different kinds of convergence appear naturally. In most cases, different kinds of convergence are associated with different vector spaces vector space -of measurable functions of (equivalence classes of) measurable functions, and it is the purpose of this chapter to describe some of these spaces and discuss the corresponding types of convergence. One of the most basic requirements for a mode of convergence is that the usual operations of addition and multiplication by scalars preserve convergence. Because of this, we will be dealing with vector spaces endowed with a topology that is compatible with the linear structure. We start therefore with a brief discussion of the concept of a topological vector space vector space -topological topological vector space . The discussion is carried out for complex vector spaces, but the analogous concepts make sense for real vector spaces as well.

Suggested Citation

  • Hari Bercovici & Arlen Brown & Carl Pearcy, 2016. "The L p spaces," Springer Books, in: Measure and Integration, edition 1, chapter 0, pages 203-239, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-29046-1_9
    DOI: 10.1007/978-3-319-29046-1_9
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    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:spr:sprchp:978-3-319-29046-1_9. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.