On projections of finitely additive measures
Thomas Jech and Karel Prikry
Proc. Amer. Math. Soc. 74 (1979), 161-165
Primary 28A12; Secondary 54H10
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Abstract: A theorem of Z. Frolík and M. E. Rudin states that for every two-valued measure on N, if is such that then for almost all x. We prove that a generalization of this theorem fails for measures in general: Theorem. There exist a translation invariant measure on N and a function such that , and if is such that F is one-to-one on A, then .
Frolík, Fixed points of maps of
𝛽𝑁, Bull. Amer. Math. Soc.
187–191. MR 0222847
(36 #5897), http://dx.doi.org/10.1090/S0002-9904-1968-11935-4
Ellen Rudin, Partial orders on the types in
𝛽𝑁, Trans. Amer. Math. Soc.
353–362. MR 0273581
(42 #8459), http://dx.doi.org/10.1090/S0002-9947-1971-0273581-5
Pincus and Robert
M. Solovay, Definability of measures and ultrafilters, J.
Symbolic Logic 42 (1977), no. 2, 179–190. MR 0480028
- Zdeněk Frolík, Fixed points of maps of , Bull. Amer. Math. Soc. 74 (1968), 187-191. MR 0222847 (36:5897)
- Mary Ellen Rudin, Partial orders on the types in , Trans. Amer. Math. Soc. 155 (1971), 353-362. MR 0273581 (42:8459)
- David Pincus and Robert M. Solovay, Definability of measures and ultrafilters, J. Symbolic Logic 42 (1977), 179-190. MR 0480028 (58:227)
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