The Bernstein polynomial is a crucial concept in approximation theory and mathematical analysis, particularly in the context of polynomial interpolation and approximation of continuous functions. The Bernstein polynomials are defined to approximate a continuous function on a closed interval [0, 1] by a weighted sum of polynomials.
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For , its tensor-product Bernstein polynomial is the expectation of for independent binomial variables . Uniform continuity and concentration of the binomial variables prove uniform convergence to .