Joint continuity of measurable biadditive mappings

Christensen, Jens Peter Reus; Fischer, Pal

doi:10.1090/S0002-9939-1988-0929436-1

Joint continuity of measurable biadditive mappings
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by Jens Peter Reus Christensen and Pal Fischer PDF

Proc. Amer. Math. Soc. 103 (1988), 1125-1128 Request permission

Abstract:

The main result of this paper is the following theorem. If ${G_1},{G_2}$ and ${G_3}$ are abelian Polish groups and $C:{G_1} \times {G_2} \to {G_3}$ is a Christensen measurable biadditive mapping, then $C$ is jointly continuous.

References

Jean Calbrix and Jean-Pierre Troallic, Applications séparément continues, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 13, A647–A648 (French, with English summary). MR 534521
Jens Peter Reus Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255–260 (1973). MR 326293, DOI 10.1007/BF02762799
J. P. R. Christensen, Topology and Borel structure, North-Holland Mathematics Studies, Vol. 10, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974. Descriptive topology and set theory with applications to functional analysis and measure theory. MR 0348724
Jens Peter Reus Christensen and Pal Fischer, Small sets and a class of general functional equations, Aequationes Math. 33 (1987), no. 1, 18–22. MR 901797, DOI 10.1007/BF01836148
T. M. K. Davison, A functional equation for quadratic forms, Aequationes Math. 21 (1980), no. 1, 1–7. MR 594087, DOI 10.1007/BF02189333
Pal Fischer and Zbigniew Słodkowski, Christensen zero sets and measurable convex functions, Proc. Amer. Math. Soc. 79 (1980), no. 3, 449–453. MR 567990, DOI 10.1090/S0002-9939-1980-0567990-5
P. Fischer and J. P. Mokanski, A class of symmetric biadditive functionals, Aequationes Math. 23 (1981), no. 2-3, 169–174. MR 689030, DOI 10.1007/BF02188029
Andrew M. Gleason, The definition of a quadratic form, Amer. Math. Monthly 73 (1966), 1049–1056. MR 207728, DOI 10.2307/2314635
Svetozar Kurepa, On the quadratic functional, Acad. Serbe Sci. Publ. Inst. Math. 13 (1961), 57–72. MR 131187
P. Jordan and J. Von Neumann, On inner products in linear, metric spaces, Ann. of Math. (2) 36 (1935), no. 3, 719–723. MR 1503247, DOI 10.2307/1968653