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7:13 AM
The fictitious mathematician John Rainwater was created as a student prank but has become known as the author of important results in functional analysis. At the University of Washington in 1952, John Rainwater was invented and enrolled in a mathematics course by graduate students who were in possession of a duplicate student-registration form. Later, mathematicians published under the pseudonym of John Rainwater. Papers were published under the name Rainwater mainly in functional analysis, particularly in the geometric theory of Banach spaces and in convex functions. Rainwater's theorem is...
Rainwater's theorem. Let $X$ be a Banach space, let $\{x_n\}$ be a bounded sequence in $X$ and $x \in X$. If $f(x_n)\to f(x)$ for every $f\in\operatorname{Ext}(B_{X^*})$, then $x_n \overset{w}\to x$.
 

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