Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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

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