Suggestions for a good Measure Theory book - MathOverflow
Without that information, the question becomes "Please list some measure theory books that some people have liked", which is pretty close to just "Please list some measure theory books". Even a community wiki question should have more of a focus than this, IMO. $\endgroup$
Newest 'measure-theory' Questions - MathOverflow
According to the 7.2.2 Theorem of the book "Measure Theory" written by V.I. Bogachev, every tight $\tau$-additive finite measure is Radon. The proof says: "The restrictions of a $\tau$-... measure-theory
measure theory - Fubini's theorem without completeness or …
So I propose to define the product measure always on $\Sigma_0$. We get the usual definition in the $\sigma$-finite case. In other case we get always Fubini-Tonelli and Tonelli theorems without restrictions. I have experimented this many times in my classes of Measure Theory (now dead by Bolonia reform).
Measure theory and number theory? - Physics Forums
2007年11月21日 · Now, on to measure theory and number theory! So, the first thing to note is that people often associate measure theory with real analysis because the first thing anyone did with it was generalize the definition of integration, and most of the early and famous applications of measure theory were of purely analytic, or geometric-analytic, interest.
Measure Theories with a different convention to - MathOverflow
2020年5月13日 · As we all know in a first course in measure theory we define a symbol $\infty$ to satisfy $\infty \cdot 0=0$, but there are more two possible choices for a convention as someone has shown to me; one is $\infty\cdot 0 =\infty$ and the other $\infty \cdot 0 =-\infty$.
measure theory - Quotients of Measurable Spaces? - MathOverflow
This seems to be the most natural way to construct a quotient of a measurable space. I'm sure someone must have used this construction before, but I couldn't find a single paper making use of it. In general, outside of statistical decision theory and topological measure theory, there seems to be little work on measurable spaces in themselves.
measure theory - Non-Borel sets without axiom of choice
Measure theory without the Axiom of Choice (not even countable choice) is discussed in Fremlin, Measure Theory, Volume 5, Chapter 56. This is freely available online. Thanks to MO and ex-falso-quodlibet for making me aware of this extensive text in this answer.
measure theory - Product of Borel sigma algebras - MathOverflow
The answer to question 3 is yes. At least according to Lemma 6.4.2 of the second volume of Bogachev's book "Measure Theory". He requires both spaces to be Hausdorff and one of them to have a countable base. They need not be metric spaces.
measure theory - Relationship of Baire sets and Baire functions ...
2019年6月14日 · Halmos Measure Theory has a problem (51.6) which goes as follows: The term "Baire set" is suggested by the term "Baire function" as used in analysis. If $\mathscr{B}$ is the smallest class of funct...
terminology about ring/algebra in abstract algebra and measure …
2010年4月27日 · $\begingroup$ Thank you but, to be more specific, my intention is to compare "ring in measure theory" with "ring in abstract algebra", not "ring" with "algebra". I use notation "ring/algebra" in the post because the term algebra has the same situation, that is, compare "algebra in measure theory" with "algebra in abstract algebra". $\endgroup$