Tagged Questions
5
votes
1answer
88 views
Homogenous measure on the positive real halfline
Define a measure $\mu\not=0$ on positive real number $\Bbb R_{>0}$ such that for any measurable set $E\subset\Bbb R_{>0}$ and $a\in \Bbb R_{>0} $, we have $\mu(aE)= \mu(E)$, where ...
1
vote
1answer
56 views
Null sets of $\sigma$-algebras generated by functionals
These are some questions that I couldn't answer after a class I'm teaching. I would very much appreciate help.
Let $\Omega=[0,1]^N$ and suppose that $f,g\colon \Omega \to [0,1]^N$ are two functions ...
4
votes
0answers
100 views
Three properties of the Lebesgue measure on $\mathbb{R}^n$
I'm writing notes for my upcoming class in Game Theory and I realized some time ago that I only need three properties of the Lebesgue measure $\lambda$ on $\mathbb{R^n}$.
It is a non-negative ...
