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Kraft's inequality limits the lengths of codewords in a prefix code: if one takes an exponential of the length of each valid codeword, the resulting set of values must look like a probability mass function, that is, it must have total measure less than or equal to one. Kraft's inequality can be thought of in terms of a constrained budget to be ...
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In mathematics, Grönwall's inequality (also called Grönwall's lemma or the Grönwall–Bellman inequality) allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation. There are two forms of the lemma, a differential form and an ...
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 ().
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