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We propose a new framework for cooperative spectrum sensing in cognitive radio networks, that is based on a novel class of nonuniform samplers, called the event-triggered samplers, and sequential detection. In the proposed scheme, each secondary user (SU) computes its local sensing decision statistic based on its own channel output; and whenever such decision statistic crosses certain predefined threshold values, the secondary user will send one (or several) bit of information to the fusion center (FC). The FC asynchronously receives the bits from different SUs and updates the global sensing decision statistic to perform a sequential probability ratio test (SPRT), to reach a sensing decision. We provide an asymptotic analysis for the above scheme, and under different conditions, we compare it against the cooperative sensing scheme that is based on traditional uniform sampling and sequential detection. Simulation results show that the proposed scheme, using even 1 bit, can outperform its uniform sampling counterpart that uses infinite number of bits under changing target error probabilities, SNR values, and number of SUs.