Extending a measure from a ring to a sigma-ring

Johnson, Roy A.

doi:10.1090/S0002-9939-1980-0567986-3

Extending a measure from a ring to a sigma-ring
HTML articles powered by AMS MathViewer

by Roy A. Johnson PDF

Proc. Amer. Math. Soc. 79 (1980), 431-434 Request permission

Abstract:

For each measure on a ring, there is a smallest measure on the generated sigma-ring such that ring members of finite measure keep the same measure. Conditions are given under which this smallest semi-extension preserves sums and order.

References

Sterling K. Berberian, Measure and integration, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1965. MR 0183839
Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
Deng Yuan Huang, A note on generalized unique extension of measures, J. Austral. Math. Soc. 14 (1972), 59–61. MR 0315078
Norman Y. Luther, Unique extension and product measures, Canadian J. Math. 19 (1967), 757–763. MR 217247, DOI 10.4153/CJM-1967-069-7
A. Mukherjea and K. Pothoven, Real and functional analysis, Mathematical Concepts and Methods in Science and Engineering, Vol. 6, Plenum Press, New York-London, 1978. MR 0492145
H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555