Essays about: "Lebesgue point"

Found 3 essays containing the words Lebesgue point.

  1. 1. Dynamical Behaviors of A Class of Generalized Skew Shifts

    University essay from KTH/Matematik (Avd.)

    Author : Kuan Yan; [2022]
    Keywords : mathematics; dynamical systems; skew shifts; SNAs; matematik; dynamiska system; skeva skift; SNAs;

    Abstract : In this paper we study a dynamical system given by a variant of the classic skew-shifts on the torus $S^1\times S^1$. Our map is defined based on $T(x,y) = (x+\omega,x+f(y))$, where $\omega$ is Diophatine, $f$ is an orientation-preserving circle diffeomorphism. READ MORE

  3. 2. The Henstock–Kurzweil Integral

    University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Author : Manolis David; [2020]
    Keywords : Henstock–Kurzweil integral; generalized Riemann integral; gauge integral; Denjoy–Perron integral; narrow Denjoy integral; Perron integral; non-absolute integration; Lebesgue outer measure; absolute integrability; fundamental theorem of calculus; convergence theorems; single variable calculus;

    Abstract : Since the introduction of the Riemann integral in the middle of the nineteenth century, integration theory has been subject to significant breakthroughs on a relatively frequent basis. We have now reached a point where integration theory has been thoroughly researched to a point where one has to delve quite deep into a particular subject in order to encounter open conjectures. READ MORE

  4. 3. Lebesgue points, Hölder continuity and Sobolev functions

    University essay from Matematiska institutionen

    Author : John Karlsson; [2009]
    Keywords : Lebesgue point; Hausdorff dimension; Hausdorff measure; Hölder continuity; Maximal function; Poincaré inequality; Sobolev space; Uniform continuity;

    Abstract : This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L1 functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. READ MORE