  On a Riemannian metric-measure space, we establish an
Alexandrov-Bakelman-Pucci type measure estimate connecting Bakry-\'Emery Ricci
curvature lower bound, modified Laplacian and the measure of certain special
sets. We apply this estimate to prove Harnack inequalities for the modified
Laplacian operator and fully non-linear operators. These inequalities seem not
available in the literature; And our proof, solely based on the ABP estimate,
does not involve any Sobolev inequalities nor gradient estimate. We also
propose a question regarding the characterization of Ricci lower bound by the
Harnack inequality.
