Elementary proof of the Rudin-Carleson and the F. and M. Riesz theorems
Elementary proof of the Rudin-Carleson and the F. and M. Riesz theorems
A very elementary proof is given of the theorem that on a set of measure zero on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T"> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding="application/x-tex">T</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, any continuous function is equal to a continuous function of analytic type. The same elementary method proves that a measure …