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Primitives and Integrals

  • Elementary Theory
  • Philip Spain

Abstract

Unless expressly mentioned to the contrary, in this chapter we shall only consider vector functions of areal variable which take their values in a complete normed space over R. When we deal in particular with real-valued functions it will always be understood that these functions are finite unless stated to the contrary.

Keywords

Compact Subset Vector Function Regulate Function Step Function Real Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Recall (Set Theory, III, p. 144) that a set a of subsets of I is directed with respect to the relation ⊂ if, for any X ∈ F, Y ∈ F, there exists Z ∈ F such that X ⊂ Z and Y ⊂ Z. If S(X) denotes the subset of F formed by the U ∈ F such that UX, then the S(X) form a base for a filter on F, called the filter of sections of F the limit (if it exists) of a map f of F into a topological space, with respect to the filter of sections of F, is called the limit off with respect to the directed set F (cf. Gen. Top., I, p. 70 and Gen. Top., IV, p. 348).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Elementary Theory
  • Philip Spain
    • 1
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowScotland

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