The measure-theoretic aspects of entropy, part I

On Measure-Theoretic aspects of Nonextensive Entropy Functionals and corresponding Maximum Entropy Prescriptions

Shannon entropy of a probability measure P , defined as − ∫ X dP dμ ln dP dμ dμ on a measure space (X,M, μ), is not a natural extension from the discrete case. However, maximum entropy (ME) prescriptions of Shannon entropy functional in the measure-theoretic case are consistent with those for the discrete case. Also it is well known that Kullback-Leibler relative entropy can be extended natural...

Wireless Information-Theoretic Security - Part I: Theoretical Aspects

In this two-part paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an information-theoretic problem formulation in which two legitimate partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through another independent quasi-static fading channel. We define the secrecy capacity in te...

Measure-Theoretic Probability I

Measure Theoretic Aspects of Dynamical Systems

In this exposition, we will present the fundamental theorem in Ergodic theory and its applications.

Part I Set Theoretic Topology