  With a view toward fractal spaces, by using a Korevaar-Schoen space approach,
we introduce the class of bounded variation (BV) functions in a general
framework of strongly local Dirichlet spaces with a heat kernel satisfying
sub-Gaussian estimates. Under a weak Bakry-\'Emery curvature type condition,
which is new in this setting, this BV class is identified with a heat semigroup
based Besov class. As a consequence of this identification, properties of BV
functions and associated BV measures are studied in detail. In particular, we
prove co-area formulas, global $L^1$ Sobolev embeddings and isoperimetric
inequalities. It is shown that for nested fractals or their direct products the
BV class we define is dense in $L^1$. The examples of the unbounded Vicsek set,
unbounded Sierpinski gasket and unbounded Sierpinski carpet are discussed.
