@article{697865,
      recid = {697865},
      author = {Lerner, Nicolas,},
      title = {A course on integration theory including more than 150  exercises with detailed answers / [electronic resource] :},
      pages = {1 online resource.},
      abstract = {This textbook provides a detailed treatment of abstract  integration theory, construction of the Lebesgue measure  via the Riesz-Markov Theorem and also via the Carathodory  Theorem. It also includes some elementary properties of  Hausdorff measures as well as the basic properties of  spaces of integrable functions and standard theorems on  integrals depending on a parameter. Integration on a  product space, change-of-variables formulas as well as the  construction and study of classical Cantor sets are treated  in detail. Classical convolution inequalities, such as  Young's inequality and Hardy-Littlewood-Sobolev inequality,  are proven. Further topics include the Radon-Nikodym  theorem, notions of harmonic analysis, classical  inequalities and interpolation theorems including  Marcinkiewicz's theorem, and the definition of Lebesgue  points and the Lebesgue differentiation theorem. Each  chapter ends with a large number of exercises and detailed  solutions. A comprehensive appendix provides the reader  with various elements of elementary mathematics, such as a  discussion around the calculation of antiderivatives or the  Gamma function. It also provides more advanced material  such as some basic properties of cardinals and ordinals  which are useful for the study of measurability.},
      url = {http://library.usi.edu/record/697865},
      doi = {https://doi.org/10.1007/978-3-0348-0694-7},
}