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Show the proof that a god exists.

Show the proof that you exist. Or that anything else exists, for that matter. Remember, the senses can be fooled; while dreaming, a dreamer cannot distinguish the sensations experienced in his dream from the sensations he perceives when awake. Any real proof has to be objective proof — i.e. proof gained without the use of the senses, which are organs of subjective perception.

What device can measure and detect it?

What device can measure and detect your own consciousness? You can't see your own mind, after all; you can't smell, touch, taste, or feel your own consciousness. (Brain electrochemistry can be detected, but brain electrochemistry is not the same thing as consciousness, else we would be able to re-animate the dead by tinkering their brains.)

Answer this question: How do you know that you exist?

What other non-measurable things do you "believe" in? Zeus? Allah?

God, i.e. the Christian Trinity. Dreams. Ideas. Love. Other people. Adam_az. The universe outside my own mind. None of these things can be measured or observed using our senses — yet I believe ( = an act of faith ) that all are real.

And so do you. You, too, are a believer. Without the slightest shred of physical evidence, you take it on faith that you are not dreaming, hallucinating, or floating in a sensory-deprivation tank jacked into a Matrix-like virtual world. You accept as a matter of blind faith that the world is real, that other people exist, and that what you perceive subjectively via your senses bears some relationship to an outside Reality.

But you can't prove it. And neither can anyone else. Since our senses can be fooled, any “proof” perceived through them is ultimately unreliable. In fact, the only thing we can know objectively is that which we perceive objectively, directly, without the use of our subjective sensory perceptions: in other words, we can only know that we ourselves exist.

Descartes put it best: Cogito, ergo sum, “I think, therefore I am”. We do not perceive our selves; we are ourselves. The fact that you can hear yourself think, see things in your mind's eye, and experience tastes, smells, and textures from days long past proves beyond any doubt that an adam_az exists somewhere. To say otherwise is to deny that oneself exists — and, by extension, that anything whatsoever exists. I trust your skepticism does not extend that far.