Coding discretizations of continuous functions

We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical continuous function when the diameter of the discretization tends to zero. Our main result is that any finite word appears on a subsequence discretization with any desired limit frequency.

• Type: Journal
• Year: 2011
• Where: DM
• Authors: Cristobal Rojas, Serge Troubetzkoy
• Keywords: Continuous Function, DM 2011, Education, Typical Continuous Function, finite Word