Local Integration of Differential Forms

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 142)


We recall that a set has measure 0 in R n if and only if, given e, there exists a covering of the set by a sequence of rectangles {R j } such that ∑ μ(R j ) < ε. We denote by R j the closed rectangles, and we may always assume that the interiors R j 0 = Int(R j ) cover the set, at the cost of increasing the lengths of the sides of our rectangles very slightly (an ε2 n argument). We shall prove here some criteria for a set to have measure 0. We leave it to the reader to verify that instead of rectangles, we could have used cubes in our characterization of a set of a measure 0 (a cube being a rectangle all of whose sides have the same length).


Dual Space Differential Form Lipschitz Condition Coordinate Function Variable Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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