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Certain Integral Equalities which Imply Equimeasurability of Functions

Published online by Cambridge University Press:  20 November 2018

Kenneth Stephenson
Kenneth Stephenson*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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1.1. Two complex measurable functions/ and g on complex measure spaces (X, η) and (Y, v) are equimeasurable, abbreviated ƒ ∼ g, if

for every Borel set E ⊆ C. If Φ is a continuous complex function on C, then we make the following standing hypothesis (HI) which relates Φ, f, and g:

(HI) For all α, β ∊ C, we have

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 827 - 844
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Andersen, Kenneth F., OnLp norms and the equimeasur ability of functions, Proc. Amer. Math. Soc. Ifi (1973), 149–153.Google Scholar
2. Forelli, Frank, The isometries of Hp, Can. J. Math. 16 (1964), 721–728.Google Scholar
3. Forelli, Frank A theorem on isometries and the application of it to the isometries of HP(S).Google Scholar
4. Forelli, Frank p < oo, Can. J. Math. 25 (1973), 284–289.Google Scholar
5. Lamperti, John, On the isometries of certain function-spaces, Pac. J. Math. 8 (1958), 459–466.Google Scholar
6. Rudin, Walter, LP-isometries and equimeasur ability, Indiana University Math. J. 25 (1976), 215–228.Google Scholar
7. Schneider, Robert B., Unit preserving isometries are homomorphisms in certain Lp, Can. J. Math. 27 (1975), 133–137.Google Scholar
8. Schwartz, Laurent, Sur certaines familles non fondamentales de fonctions continues, Bull. Soc. Math. France, 72 (1944), 141–144.Google Scholar
9. Widder, D. V., An introduction to transform theory (Academic Press, New York, 1971).Google Scholar
10. Zalcman, Lawrence, Analyticity and the Pompeiu problem, Arch. Rat. Mech. Anal. 18 (1972), 237–254.Google Scholar