【摘要】 设f∈L_p\R_m¹,p≥1。如果f在R_m¹中有无穷多个最佳逼近,则这些最佳逼近必有一致收敛的子序列,并且其极限函数也是f的最佳逼近。如果f在R_m¹中的最佳逼近都是非退化的临界点,则这些最佳逼近仅有有限个。f在R_m¹中的形如P₁（x）/（1-λx）ⁿ的最佳逼近仅有有限个。更多还原

【Abstract】 Let f∈L_p\R_m^l If f has infinitely many best approximations in R_m^l, then they have a subsquence which is uniformly convergent and their limit is also the best approximation to f. If all the best approximations to f are nondegenerate critical points, then the number of the best approximations is finite. The number of the best L₂-approximation in R_<sup>l such as P_t（1—λ_x）ⁿ is finite.更多还原