On integration with respect to filter

TL;DR

This paper introduces a generalized form of integration called filter integration, extending the Riemann integral by using filters, and explores its properties and phenomena.

Contribution

It proposes a novel generalization of the Riemann integral through filter-based integration and analyzes its mathematical properties.

Findings

Filter integration generalizes Riemann integral.

Different properties and phenomena of filter integration are demonstrated.

Abstract

Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and phenomena of filter integration.