Either we define discontinuous functions or multivalued functions.
2.
But on top of that, you want pointwise convergence to a discontinuous function.
3.
BBO can therefore be used on discontinuous functions.
4.
As well as introducing discontinuous functions, as we discussed above, he conceived the calculus as operational symbols.
5.
An even more general result is the Carath�odory existence theorem, which proves existence for some discontinuous functions ?.
6.
If the law of the excluded middle held, then this would be a fully defined, discontinuous function.
7.
It extends the classical finite element method by enriching the solution space for solutions to differential equations with discontinuous functions.
8.
The construction of discontinuous functions fails because a function is identified with a curve, and the curve cannot be constructed pointwise.
9.
Arbogast won the prize with his essay and his notion of discontinuous function became important in Cauchy's more rigorous approach to analysis.
10.
It extends the classical finite element method ( FEM ) approach by enriching the solution space for solutions to differential equations with discontinuous functions.
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