Left invariant measures on locally compact fan loops

TL;DR

This paper investigates the existence and properties of left invariant measures on locally compact fan loops, a class of nonassociative algebraic structures, and explores their construction through various product operations.

Contribution

It proves the existence of nontrivial left invariant measures on locally compact fan loops and develops methods to construct many such loops via product operations.

Findings

Existence of nontrivial left invariant measures is established.

Properties and estimates of functions on fan loops are analyzed.

Construction of abundant fan loops through products is demonstrated.

Abstract

In this article left invariant measures and functionals on locally compact nonassociative fan loops are investigated. For this purpose necessary properties of topological fan loops, estimates and approximations of functions on them are studied. An existence of nontrivial left invariant measures on locally compact fan loops is proved. Abundant families of fan loops are provided with the help of different types of their products.