Ask the definition of monotone likelihood ratio (MLR)

Question

The defintion is from George Casella textbook definition 8.3.16. It says a family of pdfs or pmfs {$g(t|\theta):\theta \in \Theta$} for a univariate random variable T with real-valued parameter $\theta$ has a monotone likelihood ratio (MLR) if for every $\theta_2 > \theta_1 $, $g(t|\theta_2)/g(t|\theta_1)$ is a monotone (nonincreasing or nondecreasing) function of t on {$t: g(t|\theta_1)>0$ or $g(t|\theta_2)>0 $}. Note that c/0 is defined as $\infty$ if 0<c.

My questions:

1. What's the meaning of univariate random variable T?

2. Why do we need the condition "on {$t: g(t|\theta_1)>0$ or $g(t|\theta_2)>0 $}"?

3. Why do we need "Note that c/0 is defined as $\infty$ if 0<c"?

4. Do we need to restrict the number of $\theta$ parameter? i.e., we only have one unknown parameter. We cannot have more than one unknown $\theta$, if we want to claim some pdfs are MLR.