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    STUDIA MATHEMATICA - Issue no. 2 / 2013  
         
  Article:   A SIMPLE PROOF OF THE FUNDAMENTAL THEOREM OF CALCULUS FOR THE LEBESGUE INTEGRAL.

Authors:  .
 
       
         
  Abstract:  

This paper contains a new elementary proof of the Fundamental Theorem of Calculus for the Lebesgue integral. The hardest part of our proof simply concerns the convergence in L1 of a certain sequence of step functions, and we prove it using only basic elements from Lebesgue integration theory.

Mathematics Subject Classification (2010): 26A46, 26A36.

Keywords: Fundamental theorem of calculus, Lebesgue integral, absolute continuity.

 
         
     
         
         
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