14 citations · 44 across the 14 of their papers we have counts for
5 papers · 1 filter
Describing limits of integrable functions as grid functions of nonstandard analysis
Emanuele Bottazzi
In functional analysis, there are different notions of limit for a bounded sequence of functions. Besides the pointwise limit, that does not always exist, the behaviour of a…
A real-valued measure on non-Archimedean field extensions of
Emanuele Bottazzi
We introduce a real-valued measure on non-Archimedean ordered fields that extend the field of real numbers . The definition of is i…
Spaces of measurable functions on the the Levi-Civita field
Emanuele Bottazzi
We introduce the spaces of measurable functions whose -th power is summable with respect to the uniform measure over the Levi-Civita field . These s…
Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations
Emanuele Bottazzi
We introduce the space of grid functions, a space of generalized functions of nonstandard analysis that provides a coherent generalization both of the space of distributions and of…
Elementary numerosity and measures
Vieri Benci, Emanuele Bottazzi, Mauro Di Nasso
In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set X which takes values in a suitable non-Archimedean field,…