On the Computational Complexity of Positive Linear Functionals on \(\mathcal{C}[0;1]\)

  • Hugo Férée
  • Martin ZieglerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)


The Lebesgue integration has been related to polynomial counting complexity in several ways, even when restricted to smooth functions. We prove analogue results for the integration operator associated with the Cantor measure as well as a more general second-order \({{\mathbf {\mathsf{{\#P}}}}} \)-hardness criterion for such operators. We also give a simple criterion for relative polynomial time complexity and obtain a better understanding of the complexity of integration operators using the Lebesgue decomposition theorem.


Polynomial Time Integration Operator Discrete Measure Input Length Oracle Access 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsTU DarmstadtDarmstadtGermany
  2. 2.Université de Lorraine, LORIA, UMR 7503Vandœuvre-lès-NancyFrance
  3. 3.InriaVillers-lès-NancyFrance
  4. 4.CNRS, LORIA, UMR 7503Vandœuvre-lès-NancyFrance
  5. 5.KAIST, School of ComputingDaejeonRepublic of Korea

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