  In this paper we firstly derive the weak elliptic Harnack inequality from the
generalized capacity condition, the tail estimate of jump measure and the
Poincar\'{e} inequality, for any regular Dirichlet form without killing part on
a measure metric space, by using the lemma of growth and the John-Nirenberg
inequality. We secondly show several equivalent characterizations of the weak
elliptic Harnack inequality for any (not necessarily regular) Dirichlet form.
We thirdly present some consequences of the weak elliptic Harnack inequality.
