The paper proves a nonlinear Kolmogorov weak law of large numbers under a tail condition and nonlinear independence, with no first moment required.
Kolmogorov, Sur la loi de grands nombres, Atti Accad
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On nonlinear weak law of large numbers
The paper proves a nonlinear Kolmogorov weak law of large numbers under a tail condition and nonlinear independence, with no first moment required.