Characteristic Function (convex Analysis) - Relationship With The Indicator Function

Relationship With The Indicator Function

Let denote the usual indicator function:

If one adopts the conventions that

  • for any, and ;
  • ; and
  • ;

then the indicator and characteristic functions are related by the equations

and

Read more about this topic:  Characteristic Function (convex Analysis)

Famous quotes containing the words relationship with, relationship and/or function:

    I began to expand my personal service in the church, and to search more diligently for a closer relationship with God among my different business, professional and political interests.
    Jimmy Carter (James Earl Carter, Jr.)

    Harvey: Oh, you kids these days, I’m telling you. You think the only relationship a man and a woman can have is a romantic one.
    Gil: That sure is what we think. You got something better?
    Harvey: Oh, romance is very nice. A good thing for youngsters like you, but Helene and I have found something we think is more appropriate to our stage of life—companionship.
    Gil: Companionship? I’ve got a flea-bitten old hound at home who’ll give me that.
    Tom Waldman (d. 1985)

    To look backward for a while is to refresh the eye, to restore it, and to render it the more fit for its prime function of looking forward.
    Margaret Fairless Barber (1869–1901)