| 1. | Hence, all the special preservation properties stated above induce monotonicity.
|
| 2. | It is noted that monotonicity properties, etc . ).
|
| 3. | Thus monotonicity does not have to be included in the definition explicitly.
|
| 4. | One can examine a function's monotonicity without calculus.
|
| 5. | Again, half-way monotonicity is incompatible with the Condorcet criterion.
|
| 6. | It is truthful because the median function satisfies the strong monotonicity property.
|
| 7. | APV satisfies the monotonicity criterion, the participation criterion and the consistency criterion.
|
| 8. | A result of Geroch implies that Hawking mass satisfies an important monotonicity condition.
|
| 9. | Again, a similar reasoning yields monotonicity of.
|
| 10. | Note that this property implies monotonicity of ?.
|
