  For Green-Schwarz superstring sigma-model on curved backgrounds, we introduce
a non-metric measure $\Phi \equiv \epsilon^{i j} \epsilon^{I J} (\partial_i
\varphi^I) (\partial_j \varphi^J)$ with two scalars $\varphi^I (I = 1, 2)$ used
in Two Measure Theory (TMT). As in the flat-background case, the string tension
$T= (2 \pi \alpha ' )^{-1}$ emerges as an integration constant for the
A_i-field equation. This mechanism is further generalized to supermembrane
theory, and to super p-brane theory, both on general curved backgrounds. This
shows the universal applications of dynamical measure of TMT to general
supersymmetric extended objects on general curved backgrounds.
