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Measurable Spaces
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Measure Theory JohnK.Hunter - Mathematics Home
www.math.ucdavis.eduMeasurable spaces provide the domain of measures, defined below. Definition 1.5. A measurable space (X,A) is a non-empty set Xequipped with a σ-algebra A on X. It is useful to compare the definition of a σ-algebra with that of a topology in Definition 1.1. There are two significant differences. First, the complement of a
90 - University of California, Davis
www.math.ucdavis.edu) is the space of essentially bounded Lebesgue measurable functions on with the essential supremum as the norm. The spaces Lp() are Banach spaces for 1 p 1. Example 5.7 The Sobolev spaces, Wk;p, consist of functions whose derivatives satisfy an integrability condition. If (a;b) is an open interval in R, then we de ne