an elementary proof of lebesgue's differentiation theorem
an elementary proof of lebesgue's differentiation theorem
an elementary proof of lebesgue's differentiation theorem
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In our work we proved this result with using <strong>elementary</strong> consepts. We usedsets <strong>of</strong> measure zero, Heine-Borel Theorem, upper <strong>an</strong>d lower derivatives whichc<strong>an</strong> be presented in <strong>an</strong> <strong>elementary</strong> <strong>an</strong>alysis course. Mathematici<strong>an</strong>s workedto prove this result m<strong>an</strong>y times in m<strong>an</strong>y ways. For inst<strong>an</strong>ce a geometric<strong>pro<strong>of</strong></strong> was given by D. Austin. But the arguments in this work are morecomplicated to underst<strong>an</strong>d. It c<strong>an</strong> be <strong>an</strong>other work to study solely.References[1] M. W. Botsko. An Elementary Pro<strong>of</strong> <strong>of</strong> Lebesgue’s Differentiation Theorem,The Americ<strong>an</strong> Mathematical Monthly, 110 (9), (Nov 2003): 834-838.[2] R. P. Boas., A Primer <strong>of</strong> Real Funtions,(Rahway, New Jersey: MathematicalAssociation <strong>of</strong> America, 1960).9
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