## The Entropy of Linear Cellular Automata with Respect to Any Bernoulli Measure

**Hasan Akin***Department of Mathematics**Arts and Science Faculty**Harran University, Sanliurfa, 63120, Turkey**akinhasan@harran.edu.tr*

#### Abstract

This paper deals with the measure-theoretical entropy of a linear cellular automaton (LCA) , generated by a bipermutative local rule (*m* ≥ 2 and l, ), with respect to the Bernoulli measure on defined by a probability vector . We prove that the measure entropy of the one-dimensional LCA with respect to any Bernoulli measure is equal to .