Measurable Functions

  • Boris Makarov
  • Anatolii Podkorytov
Part of the Universitext book series (UTX)


We introduce the notion of a measurable function needed in the construction of the integral, study the properties of measurable functions and different types of convergence for sequences of measurable functions. We prove the important theorem of Egorov, which reduces pointwise convergence to uniform convergence by deleting an appropriate set of arbitrarily small measure. We discuss the question of approximation of measurable functions by continuous ones.


Measurable Function Uniform Convergence Simple Function Zero Measure Inverse Image 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Boris Makarov
    • 1
  • Anatolii Podkorytov
    • 1
  1. 1.Mathematics and Mechanics FacultySt Petersburg State UniversitySt PetersburgRussia

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