How you are with $\mathfrak{s}$ and $\mathfrak{r}$?

TL;DR

This paper explores the implications of real-valued measurable cardinals on certain cardinal characteristics of the continuum, establishing specific equalities under these assumptions.

Contribution

It proves that the existence of a real-valued measurable cardinal implies the splitting number is  and the reaping number equals the continuum.

Findings

If a real-valued measurable cardinal exists, the splitting number is .

If the continuum is real-valued measurable, then the reaping number equals the continuum.

Abstract

We prove that if there is a real-valued measurable cardinal then the splitting number is $\aleph_1$. Likewise, if the continuum is real-valued measurable then the reaping number equals the continuum.