We address the problem of testing for mutual independence of several functional random variables.We first introduce a pairwise independence measure for more than two random elements that aggregates the independence measures between pairs of random elements. From this,we derive an asymptotically normal test statistic, enabling a straightforward testing procedure that avoids the need for permutation or bootstrap resampling techniques. Finally, the proposed testing procedure is extended to handle mutual independence through both asymmetric and symmetric aggregation methods.