Search results with tag "Baire category theorem"
The Baire category theorem - UCL
www.ucl.ac.ukTheorem 7.3 (Baire category theorem) Let X be a complete metric space. Then: (a) A meager set has empty interior. (b) The complement of a meager set is dense. (That is, a residual set is dense.) (c) A countable intersection of dense open sets is dense.
Chapter 3 The Space of Continuous Functions
www.math.cuhk.edu.hkBaire category theorem is proved and, as an application, it is shown that continuous, nowhere di erentiable functions form a set of second category in the space of continuous functions. 3.1 Spaces of Continuous Functions We studied continuous functions on an interval in MATH2050/60 and in a domain bounded
Measure Measure - Department of Mathematics
math.unl.eduBaire, Sur les fonctions de variables r´eelles, Ann.di Mat.(3), III (1899), 1–123. Contains, among other things, the “Osgood-Baire Category Theorem” on R n . 3.
The Baire category theorem - UCL
www.ucl.ac.ukRemark. If you have studied Measure Theory, then you have encountered another important σ-ideal of sets in R or Rn, namely the sets of Lebesgue measure zero (also called null sets). These sets are “negligible” in the measure-theoretic sense.