Tagged Questions

6
votes
2answers
109 views

It is possible to define our intuitive notion for probability in subsets of $[0,1]$

I've always heard and read the sentence: If you pick a real number $x\in[0,1]$ at random, the probability to obtain a rational number is $0$. What is the meaning for that? Is this the "real" ...
0
votes
1answer
26 views

Difference in reference of L space in Fubini Tonelli

I think my understanding of how $L^+$ and $L^1$ spaces are defined (I'm using Folland) is a little hazy. For example, in the Fubini-Tonelli theorem: $\textbf{For the Tonelli part:}$ We start with if ...
0
votes
1answer
32 views

Proposition from the book “Convex analysis and measurable multifunction ”

Please , what is $F_{\sigma}$? And all $U$ can be writen as $\cup F_n$, or only open set ? Thank you
2
votes
0answers
78 views

Exercise on measure theory

I have this exercise: from the book "Measure theory ; Donald L. Cohn" I don't know what $\sigma(...)$ is? Thank you.
3
votes
2answers
49 views

Definition of complete in the context of Lebesgue measurable sets

I came across this statement on Lebesgue measurable sets. The Lebesgue measurable sets are said to be complete because every subset of a null set is again measurable and the lebesgue measurable ...
1
vote
0answers
32 views

What is the appropriate def. of $\sigma$-($\Sigma^1_1$) measurable.

I know that borel measurable means that the inverse image of a Borel set (or open set) is measurable. Edit: I am speaking of the sigma algebra generated by the analytic sets in a top. space.
4
votes
1answer
133 views

What is “algebra” in $\sigma$-algebra (or “field” in $\sigma$-field)?

I know that $\sigma$ in $\sigma$-algebra stands for the closure under countable union property. What about "algebra"? Surely it cannot algebra over a field or a ring as defined in algebra textbooks. ...
1
vote
2answers
141 views

Measure and Outer Measure Definition

I would like to find exemples to show and demonstrate that each of the statements of the definition of: -measure $\mu\left(\emptyset \right)=0$ $\mu \left( \bigcup A_n\right)=\sum \mu \left( ...
1
vote
1answer
70 views

Meaning of Point Evaluation

I read in some general measure theory books and there is always like "define measure $x$ to be the point evaluation at $y$..." but when I look around online and some other books there is no mention on ...
2
votes
4answers
86 views

What are possible variations of the definition of $\sigma$-additivity?

From what I've read in Wikipedia, $\sigma$-additivity is defined in the following way: Let $\mathcal{A}$ be a $\sigma$-algebra of some underlying set $X$ and let $f$ be a mapping ...
2
votes
0answers
53 views

terminology clarification needed: projection of a measure to an open set

I'm reading in Doobs "Classical Potential Theory and its Probabilistic Counterpart" and I'm having trouble with terminology. Specifically, in Part I chapter 6, he talks about the projection of a ...
6
votes
1answer
487 views

what is f prime?

currently taking Measure and Integration course, which seems to have a different definition of f'. traditionally, $$f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$$ but in folland's book, it seems ...