Relationship between the principle of least effort and the average cost of information in a zipfian context

From an informetrics perspective, we discuss the relationship between the Least Effort Principle and information cost minimisation, and discuss the implications for Zipf's law. We propose a mathematical proof of a theorem demonstrating that if one minimises the average cost per unit of information, the Least Effort Principle (LEP) will be verified regardless of the effort function chosen. We then show that Zipf's law can be demonstrated on the basis of the two models studied, namely Average Cost per Unit of Information and the Least Effort Principle (LEP).