Lots of the exact same entropy measures in classical details concept can be generalized towards the quantum circumstance, like Holevo entropy and conditional quantum entropy. Quantum mutual information and facts[edit]
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In numerous von Neumann's papers, the ways of argument he employed are regarded as even more substantial than the final results. In anticipation of his later on study of dimension theory in algebras of operators, von Neumann made use of success on equivalence by finite decomposition, and reformulated the issue of evaluate in terms of capabilities.[one hundred twenty five] A serious contribution von Neumann designed to evaluate concept was the results of a paper prepared to reply an issue of Haar with regards to regardless of whether there existed an algebra of all bounded functions on the actual selection line such that they type "an entire system of Reps from the courses of virtually just about everywhere-equivalent measurable bounded capabilities".[126] He proved this during the constructive, and in later on papers with Stone mentioned different generalizations and algebraic facets of this issue.
Wigner informed an identical Tale, only using a swallow as opposed to a fly, and states it absolutely was Max Born who posed the dilemma to von Neumann in the 1920s.[453]
This function expected the creation of normal rings.[187] A von Neumann normal ring is a ring where by for every a displaystyle a
Whilst not as prolific in physics as he was in mathematics, he However made quite a few other notable contributions to it. His revolutionary papers with Subrahmanyan Chandrasekhar over the stats of the fluctuating gravitational field created by randomly distributed stars were thought of a tour de drive.[256] In this particular paper they formulated a idea of two-overall body relaxation[257] and utilized the Holtsmark distribution to product [258] the dynamics of stellar programs.[259] He wrote numerous other unpublished manuscripts on topics in stellar construction, a number of which were A part of Chandresekhar's other functions.[260][261] In certain previously operate led by Oswald Veblen von Neumann helped establish primary Strategies involving spinors that could produce Roger Penrose's twistor concept.[262][263] Substantially of this was finished in seminars executed on the IAS throughout the 1930s.
[103] The problem of the ample axiomatization of set theory was solved implicitly about twenty decades later on by Ernst Zermelo and Abraham Fraenkel. Zermelo–Fraenkel established concept provided a number of ideas that allowed for the construction in the sets Employed in the each day apply of arithmetic, but didn't explicitly exclude the potential for the existence of the set that belongs to by itself. In his doctoral thesis of 1925, von Neumann demonstrated two procedures to exclude these discover here sets—the axiom of Basis and the notion of class.[102]
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Von check this Neumann's proof inaugurated a line of study that finally led, by way of Bell's theorem along with the experiments of Alain Component in 1982, to your demonstration that quantum physics either demands a Idea of truth substantially various from that of classical physics, or ought to include things like nonlocality in obvious violation of Specific relativity.[232]
The fast way is to watch which the bicycles fulfill precisely just one hour immediately after their get started, so the fly experienced just an hour or so for his travels; The solution must as a result be 15 miles.
The John von Neumann Award on the Rajk László College or university for Advanced Scientific studies was named in his honor, and has long been provided on a yearly basis given that 1995 to professors that have built An excellent contribution to the exact social sciences and through their get the job done have strongly motivated the Experienced advancement and pondering the members of the school.[488]