Integration of measures

Nicolas Bourbaki

Chapter Chapter V in Elements of Mathematics, 2004, pp 242-363 from Springer

Abstract: Abstract Throughout this chapter, T denotes a locally compact space, μ a positive measure on T. For every subset A of a set E, ϕA denotes the characteristic function of A (if no confusion can result thereby). By numerical function, we always mean a function taking its values in $$\overline {\text{R}} $$ , thus possibly taking on the values +∞ and −∞. The set of positive numerical functions defined on E will be denoted ℱ+(E), or simply by ℱ+ no confusion can result We agree to define the products 0·(+∞) and 0·(−∞) by giving them the value 0; thus, if f is a numerical function defined on E, and A is a subset of E, fϕA denotes the function that coincides with f on A and is equal to 0 on CA. For every point a of a locally compact space, εa denotes the measure defined by placing a unit mass at the point a (Ch. III, §1, No. 3).

Keywords: Banach Space; Compact Subset; Lebesgue Measure; Compact Support; Positive Measure (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-642-59312-3_6

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