Distribution Function and Nonincreasing Rearrangement of BC-Valued Functions with B C-Measure

This paper investigates the distribution function and nonincreasing rearrangement of BC B C -valued functions equipped with the hyperbolic norm. It begins by introducing the concept of the distribution function for BC B C -valued functions, which characterizes valuable insights into the behavior and structure of BC B C -valued functions, allowing to analyze their properties and establish connections with other mathematical concepts. Next, the nonincreasing rearrangement of BC B C -valued functions with the hyperbolic norm are studied. By exploring the nonincreasing rearrangement of BC B C -valued functions, it is aimed to determine how the hyperbolic norm influences the rearrangement process and its impact on the function’s behavior and properties.