This essay is concerned with the study of inequalities on probability spaces. Mathematical structures such as equalities incorporate an expliteness that is not consistent with the vagueness that characterizes probabilistic and real phenomena. Such inequalities are a powerful tool for a mathematician, an engineer and everyone dealing with probability theory, statistics, measure spaces, information theory and many other scientific fields.
The essay consists of two chapters. In the first one, I tried to summarize some results on probability and measure theory and define the expectation operator. Its properties are discussed and some useful propositions are prooved. In the second chapter, various inequalities are discussed. Some proofs were omitted for brevity however sufficient literature is provided.
The essay consists of two chapters. In the first one, I tried to summarize some results on probability and measure theory and define the expectation operator. Its properties are discussed and some useful propositions are prooved. In the second chapter, various inequalities are discussed. Some proofs were omitted for brevity however sufficient literature is provided.
Download the PDF file from here.
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου