It is the first time I'm facing this topic. In particular, I'm studying the RIPless framework of compressive sensing presented by Emmanuel J. Candès and Yaniv Plan in the article https://arxiv.org/pdf/1011.3854.pdf . The general idea is clear to me, but I cannot prove the Incoherence Sampling Theorem with general sampling distribution. The Incoherence Sampling Theorem is the theorem 1.1 in the linked article (available also in the attached image). Can you help me setting up the theorem's proof please?

Best regards,



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