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If Kraft's inequality holds with strict inequality, the code has some redundancy. If Kraft's inequality holds with equality, the code in question is a complete code. [2] If Kraft's inequality does not hold, the code is not uniquely decodable. For every uniquely decodable code, there exists a prefix code with the same length distribution.
In mathematics and other fields, [a] a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem " or an "auxiliary theorem".
A remarkably direct existence proof was given by Martin Eichler, [12] see also the "Existence results" section below. In other cases, one may need detailed information about and it is therefore desirable to compute as explicitly as possible. Numerous formulas exist; we will describe two of the main ones (Dynkin's formula and the integral ...
In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after Pierre Fatou. Fatou's lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue's dominated convergence theorem.
This is essentially the statement of Nakayama's lemma. [17] Precisely, one has: Nakayama's lemma: Let U be a finitely generated right module over a (unital) ring R. If U is a non-zero module, then U·J(R) is a proper submodule of U. [17]
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In ergodic theory, Kac's lemma, demonstrated by mathematician Mark Kac in 1947, [1] is a lemma stating that in a measure space the orbit of almost all the points contained in a set of such space, whose measure is (), return to within an average time inversely proportional to ().
When Kraft’s attendance was confirmed at the event, roasters were allegedly … Tom Brady Roaster Says ‘They Told Us No Jokes About Happy Endings’ and Robert Kraft, Then Jeff Ross Didn’t ...