I found that in Wikipedia and many other sources Likelihood Ratio Test Statistic is defined as $$\lambda(x)=\frac{\sup_{\theta\in\Theta_1}{L(\theta)}}{\sup_{\theta\in\Theta_0}{L(\theta)}}$$ where $L(\theta)$ is the likelihood function. So the LRT is then formed as the rejection region for which the LRT statistic defined above is greater then some $k$.
On the other hand, in Statistical Inference by Casella & Berger LRT statistic is defined as $$\lambda(x)=\frac{\sup_{\theta\in\Theta_0}{L(\theta)}}{\sup_{\theta\in\Theta}{L(\theta)}}$$ and test is formed as the region for some $k \leq 1$.
The only thing I concerned is the denominator. I was pretty sure Casella & Berger is the standard textbook and so I find this deviation confusing.
Could someone experienced point out is it just a difference in style/approach to the definition or Casella & Berger actually speak about some particular approach nowadays considered a non-standard one or something else? Thank you!