# This theorem is the same as the plug-in estimator?

I'm reading this book and on page 301 he states this theorem:

I found it very similar with the plug-in estimator, the application of this theorem is the plug-in estimator?

Among things you might use that name for, this theorem is distinctive in how weak the assumptions are. $$g$$ is an arbitrary (measurable) function -- there are no assumptions that $$g$$ is (piecewise) smooth or continuous or is one:one at $$\hat\theta$$ or anything like that.