# Lebesgue Measurable Sets, Compact Sets and Open Sets

If A is lebesgue measurable sets in R^n, bounded, then there is a compact set K_epsilon and an open set for every epsilon > 0 V_epsilon such that

K_epsilon is subset of A and A is a subset of V_epsilon

and for m(A-K) < epsilon

m(V-K) < epsilon.

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Mathematics, Real Variables

lebesgue sets and compact sets problem

If A is lebesgue measurable sets in R^n, bounded, then there is a compact set K_epsilon and an open set for every epsilon > 0 V_epsilon such that

K_epsilon is subset of A and A is a subset of V_epsilon

and for m(A-K) < epsilon

m(V-K) < epsilon ...

#### Solution Summary

Lebesgue measurable sets, compact sets and open sets are investigated and discussed in the solution. The solution is detailed and well presented.