A universally measurable homomorphism between Polish groups is automatically continuous

You need to know: Groups and homomopshisms between them, topological spaces and homeomopshisms between them, continuous function on a topological space, probability measure on a topological space, metric space, complete metric space, dense subset of a metric space.

Background: A topological group G is a topological space that is also a group such that the group operations of product $G\times G \to G: (x,y) \to xy$ and taking inverses $G \to G: x \to x^{-1}$ are continuous. A topological space is called Polish space if it is homeomorphic to a complete metric space that has a countable dense subset. A Polish group is a topological group G that is also a Polish space. A Borel probability measure on a topological space is a probability measure that is defined on all open sets. A subset of a Polish group G is called universally measurable if it is measurable with respect to
every Borel probability measure on G. A homomorphism $\phi: G\to H$ between Polish groups G and H is called universally measurable if $\phi^{-1}(U)$ is a universally measurable set in G for every open set $U \subseteq H$ .

The Theorem: On 8th December 2018, Christian Rosendal submitted to the Forum of mathematics, Pi a paper in which he proved that every universally measurable homomorphism between Polish groups is automatically continuous.

Short context: The Theorem resolves a longstanding problem posed by Christensen in 1971. It can be viewed as a generalisation of old classical theorem stating that any Lebesgue measurable function $f:{\mathbb R}\to{\mathbb R}$ satisfying the functional equation $f(x+y)=f(x)+f(y), \, x,y \in {\mathbb R}$ must be continuous.