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A measurable property is a property that can be quantified using some kind of unit as a basis. For example, length is measurable, since there is a unit of length (an inch, a centimeter, etc.) and we are counting or measuring the number of units in our object. A non-measurable property is one without a standard unit. When we combine objects with a measurable property, the property must increase.
If we wanted to measure some of the properties not commonly measured, we would have to invent a method to do it. For example, to measure texture, we could look at the curvature over the small areas of the object; if the curvature doesn't change much, we could say that the texture of the object was smooth. Some interesting modern research in mathematics focuses on such "nonstandard" measurements.
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