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

Metric-Independent Measures for Supersymmetric Extended Object Theories on Curved Backgrounds