6533b835fe1ef96bd129f516

RESEARCH PRODUCT

Basic Measure Theory

Achim Klenke

subject

AlgebraProbability theoryExtension (predicate logic)Construct (philosophy)Random variableMeasure (mathematics)SemiringMathematicsProbability measure

description

In this chapter, we lay the measure theoretic foundations of probability theory. We introduce the classes of sets (semirings, rings, algebras, σ-algebras) that allow for a systematic treatment of events and random observations. Using the measure extension theorem, we construct measures, in particular probability measures on σ-algebras. Finally, we define random variables as measurable maps and study the σ-algebras generated by certain maps.

yearjournalcountryeditionlanguage
2020-01-01
https://doi.org/10.1007/978-1-4471-5361-0_1