- #1
wayneckm
- 68
- 0
Hi all,I have the following question:
Suppose there are two functions [tex]\alpha,\beta[/tex], which are both mapping [tex]\Omega \mapsto \mathbb{R}[/tex] and [tex]\alpha \leq \beta[/tex] on every point [tex]\omega \in \Omega[/tex].
I am wondering the validity of the following, for [tex]t < u[/tex],
[tex]\{t < \alpha\}\cap\{\beta<u\} = \{ t < \alpha < u\} = \{ t < \beta < u\}[/tex]
Can anyone justify this? Thanks.Wayne
Suppose there are two functions [tex]\alpha,\beta[/tex], which are both mapping [tex]\Omega \mapsto \mathbb{R}[/tex] and [tex]\alpha \leq \beta[/tex] on every point [tex]\omega \in \Omega[/tex].
I am wondering the validity of the following, for [tex]t < u[/tex],
[tex]\{t < \alpha\}\cap\{\beta<u\} = \{ t < \alpha < u\} = \{ t < \beta < u\}[/tex]
Can anyone justify this? Thanks.Wayne