A very good book is "Measure and Integration Theory" from Heinz Bauer, especially if you are planning to study probability theory. One of its strengths is that the theory is first developed …

Nov 1, 2017 · I have taken advanced courses both in measure theory and also in functional analysis (Banach and Hilbert spaces, spectral theory of bounded and unbounded operators, …

Dec 15, 2025 · Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

Dec 19, 2024 · Of course, the induced outer measure of this measure would be distinct (in particular, smaller) than $\mu^*$. This raises the following questions: Property (1) shows that …

Jan 14, 2024 · In mathematics, σ-algebras are usually studied in the context of measure theory. A separable σ-algebra (or separable σ-field) is a sigma algebra that can be generated by a …

The classic example of a non-measurable set is described by wikipedia. However, this particular construction is reliant on the axiom of choice; in order to choose representatives of …

Sep 20, 2016 · Hi, I am looking for a book for studying probability theory using measure theory. This is the first course I am taking of probability. Notions and theorems from measure theory …

Feb 16, 2025 · Explore related questions measure-theory geometric-measure-theory descriptive-set-theory hausdorff-dimension See similar questions with these tags.

In general, outside of statistical decision theory and topological measure theory, there seems to be little work on measurable spaces in themselves. To focus: Are there any papers or texts …

Mar 4, 2025 · For a deeper understanding, I would like to construct an ergodic measure preserving transformation on an infinite measure space $ (X,\mathcal F, \mu)$ that does …