Homework SourseProve that every piecewise constant function f 0 1 R can be
Prove that every piecewise constant function f : [0, 1] R can be approximated arbitrarily well (in the sense of an L1 norm) by a continuous function. (A piecewise constant function is the same as a step map, as defined on page 249 in the book). Is the same statement true if approximation is understood in the L°0 sense? the L sense? ![Prove that every piecewise constant function f : [0, 1] R can be approximated arbitrarily well (in the sense of an L1 norm) by a continuous function. (A piecew](/WebImages/22/prove-that-every-piecewise-constant-function-f-0-1-r-can-be-1054008-1761549585-0.webp "Prove that every piecewise constant function f : [0, 1] R can be approximated arbitrarily well (in the sense of an L1 norm) by a continuous function. (A piecew")
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