We continue our study of 'no-dimension' analogues of basic theorems in combinatorial and convex geometry in Banach spaces. We generalize some results of the paper \cite{ adiprasito2019theorems} and prove no-dimension versions of colorful Tverberg's theorem, selection lemma and the weak $\epsilon$-net theorem in Banach spaces of type $p > 1.$ To prove this results we use the original ideas of \cite{ adiprasito2019theorems} for the Euclidean case and our slightly modified version of the celebrated Maurey lemma.
Categories: math.MG