Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars.
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Is there some bilinear function defined on M \ times N that we can show not to be the zero function ?-- talk ) 18 : 59, 23 February 2016 ( UTC)
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His works, published in " Proceedings of the London Mathematical Society ", were " Density integration " ( 53, 1951 ); " On the measure of sum sets ( I ) The theorems of Brunn, Minkowski, and Lusternik, ( with A . M . McBeath ) " ( [ 3 ] 3, 1953 ); " Linear functions with domain a real countably infinite dimensional space " ( [ 3 ] 5, 1955 ); " Linear and bilinear functions with domain contained in a real countably infinite dimensional space " ( [ 3 ] 6, 1956 ); " The use of convergence factors in Ward integration " ( [ 3 ] 10, 1960 ); " The equivalence of generalized forms of the Ward, variational, Denjoy-Stieltjes, and Perron-Stieltjes integrals " ( [ 3 ] 10, 1960 ); " N-variation and N-variational integrals of set functions " ( [ 3 ] 11, 1961 ); " Definitions of Riemann type of the variational integrals " ( [ 3 ] 11, 1961 ); " Difference-sets and the Banach Steinhaus theorem " ( [ 3 ] 13, 1963 ); " Generalized integrals of vector-valued functions ( [ 3 ] 19 1969)
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