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I've been observing the Pix2Pix Paper - Image to Image Translation with Conditional Adversarial Networks and wondered on formulas. For example, the objective of the CGAN is: enter image description here,

where x - observed image, z - random noise, y - target image and G and D are generating and discriminating models respectively.

What does this E with "double line" stands for?

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The operator $ \mathbb{E} \left[ \cdot \right] $ is the Expectation Operator.
In the context above it means you run over all the pairs of x, y and average the values.

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