The main fundamental mathematical tools to be developed in this endeavour are a discrete analogue to the theory of regularity structures, as well as a number of nonlinear invariance principles
Merely demonstrating that Einstein's master equation of general relativity satisfies his equivalence and invariance principles takes reams of paper.
Another was the extension of the invariance principle to accelerating observers: the laws of nature themselves should be identical for all observers, regardless of the magnitude or direction of their acceleration.
They cover random systems with covariance inequalities, moment and maximal inequalities, the central limit theorem, the "almost sure" convergence, invariance principles
, the law of the iterated logarithm, statistical applications, and integral functionals.
Thus, people may be more rational than the psychological literature gives them credit for, and applications of the SEU model may be susceptible to some violations of invariance principles
Thus, the invariance principle holds in Regime D because revenue sharing has no effect on the distribution of talent and thus does not affect pre-shared club revenues.
Comment: Professional Team Sports Are Only a Game: The Walrasian Fixed-Supply Conjecture Model, Contest-Nash Equilibrium, and the Invariance Principle.
Professional Team Sports Are Only a Game: The Walrasian Fixed Supply Conjecture Model, Contest-Nash Equilibrium and the Invariance Principle.