Introductory Topics in Distributions over Binary Test Functions

Details Introductory Topics in Distributions over Binary Test Functions Introductory Topics in Distributions over Binary Test Functions

2001-10-31

arxiv.org/abs/math/0110335v1

Serban E. Vlad, Introductory Topics in Distributions over Binary Test Functions, Analele Universitatii din Oradea, Fascicola m

Mathematics

General Mathematics

the MSC-class was chosen by analogy: we refer to binary valued functions here, not to real valued functions

Scientific paper

We note with B2 the Boole algebra with two elements. We define for the R->B2 functions the limits, the derivatives, the differentiability, the test functions, the integrals. We also define the distributions over the space of these test functions, the regular and the singular distributions, the support sets of the distributions. We also define for the RxR->{0,1} functions the test functions and the distributions over them. The direct product of the distributions is presented, as well as the convolution algebras of distributions. Generalizations of the binary test functions and of the distributions over them are given.

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