additive function वाक्य

It was during this time that Henney wrote her dissertation " The theory of set-valued additive functions defined on base-cones in Banach spaces with values in the collection of compact, convex sets ".
(A consequence of this is that an additive function cannot take both & minus; & infin; and + & infin; as values, for the expression & infin; & minus; & infin; is undefined .)
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Countably additive vector measures defined on sigma-algebras are more general than finite measures, finite signed measures, and complex measures, which are countably additive functions taking values respectively on the real interval [ 0, \ infty ), the set of real numbers, and the set of complex numbers.
It can easily be seen that the latter ( linear ) representation is much more efficient in case of additive functions, as when we add many elements the latter representation will have only O ( " n " ) elements, while the former ( pointwise ), even with sharing, exponentially many.

Similarly to how exponential functions on exponential fields are defined, given a topological abelian group " G " a homomorphism from " G " to the additive group of the complex numbers is called an additive function, and a homomorphism to the multiplicative group of nonzero complex numbers is called an exponential function, or simply an exponential.