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The free will theorem states: Given the axioms, if the choice about what measurement to take is not a function of the information accessible to the experimenters (free will assumption), then the results of the measurements cannot be determined by anything previous to the experiments. That is an "outcome open" theorem:
Weak form and strong form may refer to: Weaker and stronger versions of a hypothesis, theorem or physical law; Weak formulations and strong formulations of differential equations in mathematics; Differing pronunciations of words depending on emphasis; see Weak and strong forms in English; Weak and strong pronouns
In mathematics, Serre's modularity conjecture, introduced by Jean-Pierre Serre (1975, 1987), states that an odd, irreducible, two-dimensional Galois representation over a finite field arises from a modular form. A stronger version of this conjecture specifies the weight and level of the modular form.
An abstract rewriting system is strongly normalizing, terminating, noetherian, or has the (strong) normalization property (SN), if each of its objects is strongly normalizing. [ 2 ] A rewriting system has the normal form property (NF) if for all objects a and normal forms b , b can be reached from a by a series of rewrites and inverse rewrites ...
This is a formulation of the Lax–Milgram theorem which relies on properties of the symmetric part of the bilinear form. It is not the most general form. It is not the most general form. Let V {\displaystyle V} be a real Hilbert space and a ( ⋅ , ⋅ ) {\displaystyle a(\cdot ,\cdot )} a bilinear form on V {\displaystyle V} , which is
A renewal process has asymptotic properties analogous to the strong law of large numbers and central limit theorem. The renewal function () (expected number of arrivals) and reward function () (expected reward value) are of key importance in renewal theory. The renewal function satisfies a recursive integral equation, the renewal equation.
In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, [1] [2] [3] is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. Ekeland's principle can be used when the lower level set of a minimization problems is not compact , so that the Bolzano–Weierstrass theorem ...
By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem. [1]