Abstract
An elementary content I is a real valued, non-negative, invariant and monotonous homomorphism on a decomposition structure of elementary figures. The semigroup (H,+,≤) of abstract classes is introduced (§3) by using the relation of equidecomposability and it's natural generalizations. Each elementary content divides into I=μ∘κ∘ν where κ and ν are canonical homomorphisms with respect to the relations studied before and μ: H → ℝ+ is a monotonous homomorphism called “content” (cf. Satz 3, §3). In §4 (Satz 4) the Existence-Theorem on contents is stated and it is proved in §5. The last section §6 gives the application on Archimedean decomposition structures including the case of volume measurement on polyhedrons.
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Jaritz, R. Ein Existenzsatz für Elementarinhalte. J Geom 47, 39–52 (1993). https://doi.org/10.1007/BF01223803
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DOI: https://doi.org/10.1007/BF01223803