I am reading an article which introduces the following assumption at a certain point:
The probability distribution of the (real- valued) random variable $X$ has full support and is absolutely continuous with respect to the Lebesgue measure.
I am confused on what is commonly intended by "full support". Does the author want to say that the support is $\mathbb{R}$? (which, together with absolute continuity, would then imply that the cumulative distribution function is strictly positive - and, hence, strictly monotone increasing - on $\mathbb{R}$)