A chaotic function with a distributively scrambled set of full Lebesgue measure Original Research Article

Misiurewicz proved that there exists a continuous map of the interval [0, 1] onto itself for which there exists a scrambled set of full Lebesgue measure. In this paper, we form a continuous interval map which has a distributively scrambled set of full Lebesgue measure in which each point has dense orbit. This contains Misiurewicz’s result, since any distributively scrambled set must be scrambled but the converse is not generally true.