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Figure 1 | EURASIP Journal on Wireless Communications and Networking

Figure 1

From: Optimal resource allocation in wireless communication and networking

Figure 1

Nonatomic measure. The random variable X is uniformly distributed in[0,1][2,3]. The measure w X (E):=2 E xdX is nonatomic because all sets of nonzero probability include a smaller set of nonzero probability. Lyapunov’s convexity theorem (Theorem 2) states that the measure rangeW:={ w X (E):EB} is convex. The range of w X is the, indeed convex, interval [0,3].

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