CONCERNING REAL FUNCTIONS WITH VALUES IN THE CANTOR SET

Abstract

This article in particular indicates that there exist at least continuummany "essentially nonconstant" (requiring the existence of at least two level sets having positive finite measure) almost everywhere continuous functions from the real field \(\mathbb{R}\) to the Cantor ternary set \(\mathcal{C}\), although it is a basic fact that there exists no nonconstant continuous function \(\mathbb{R} \to \mathcal{C}\).