Relaxing the ergodic-type conditions assumed in the paper would have significant implications on the error bounds and achievability of optimal performance. The ergodic conditions play a crucial role in ensuring the convergence of the error probabilities towards the Bayes error bound. By relaxing these conditions, the theoretical guarantees provided by the results may no longer hold. The error bounds may become looser, leading to potentially higher classification or regression errors. Achieving optimal performance, as defined by the Bayes error bound, may become more challenging or even unattainable without the strict ergodic-type conditions. The convergence rates towards the optimal bounds may slow down or exhibit more variability, impacting the overall performance of the classification and regression algorithms.