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A lossless antenna has directional gain $$ G(\theta,\psi)$$, then $$\int_{\psi = -\frac{\pi}{2}}^{\psi = \frac{\pi}{2}}$$ $$\int_{\theta = -\frac{\pi}{2}}^{\theta = \frac{\pi}{2}} G(\theta, \psi)d \theta d \psi$$ is:
$$4\pi$$
$$2\pi$$
$$ \leq 4\pi$$
$$ \leq 2\pi$$
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