Geodesic
Unique Extension and Product Measures
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 757-763

Voir la notice de l'article provenant de la source Cambridge University Press

Following (2) we say that a measure μ on a ring is semifinite if Clearly every σ-finite measure is semifinite, but the converse fails.In § 1 we present several reformulations of semifiniteness (Theorem 2), and characterize those semifinite measures μ on a ring that possess unique extensions to the σ-ring generated by (Theorem 3). Theorem 3 extends a classical result for σ-finite measures (3, 13.A). Then, in § 2, we apply the results of § 1 to the study of product measures; in the process, we compare the “semifinite product measure” (1; 2, pp. 127ff.) with the product measure described in (4, pp. 229ff.), finding necessary and sufficient conditions for their equality; see Theorem 6 and, in relation to it, Theorem 7. 
Luther, Norman Y. Unique Extension and Product Measures. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 757-763. doi: 10.4153/CJM-1967-069-7
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