Volume/Mass in higher dimensions.

[ProfectusInfinity]

Would a 3-Dimensional object, from the perspective of a higher dimensional space (like let's say a 5-Dimensional space), have zero voume/mass entirely? If yes, would this masslessness/volumelessness apply to all its dimensions, or just the extra ones? For example, would a 3-D being reaching 5th dimensional space have volume/mass in its 3 basic dimensions but not the 2 extra ones, or have no volume/mass in any dimension? Most importantly, what aspect of dimensional theory explains this property? Thanks in advance.

 

[Eclipso]

What you’re looking for to explain this is measure theory, not dimension theory.

An n-measure is(typically) defined on R^n, and for any usual m-dimensional subset, m<n, would have 0 n-measure(if it has any at all. There are non-measurable subsets, assuming the axiom of choice)

This is not true in general, though.

The fat cantor set is 0D, but has non-zero 1-measure(length)