Reitano R.R. Foundations of Quantitative Finance, Book I: Measure Spaces and Measurable Functions

CRC Press, 2022. - 275 p. - (Chapman & Hall/CRC Finance Series). - ISBN 1032191201.This is the first in a set of 10 books written for professionals in quantitative finance. These books fill the gap between informal mathematical developments found in introductory materials, and more advanced treatments that summarize without formally developing the important foundational results professionals need.Book I in the Foundations in Quantitative Finance Series develops topics in measure spaces and measurable functions and lays the foundation for subsequent volumes. Lebesgue and then Borel measure theory are developed on ℝ, motivating the general extension theory of measure spaces that follows. This general theory is applied to finite product measure spaces, Borel measures on ℝn, and infinite dimensional product probability spaces.Author Bio.The Notion of Measure.
Lebesgue Measure on R.
Measurable Functions.
Littlewood’s Three Principles.
Borel Measures on R.
Measures by Extension.
Finite Products of Measure Spaces.
Borel Measures on Rn.
Infinite Product Spaces.True PDF