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Let [math]T[/math] be a stopping time and [math]\Lambda\in\F_T[/math]. Define

[[math]] T_\Lambda(\omega)=\begin{cases}T(\omega)&\text{if $\omega\in\Lambda$}\\ \infty&\text{if $\omega\not\in\Lambda$}\end{cases} [[/math]]

Prove that [math]T_\Lambda[/math] is a stopping time.