In this note we show the characteristic function of every indecomposable set F in the plane is BV equivalent to the characteristic function a closed set See Formula in PDF \hbox{See Formula in PDF} . We show by example this is false in dimension three and above. As a corollary to this result we show that for every ϵ > 0 a set of finite perimeter S can be approximated by a closed subset See Formula in PDF \hbox{See Formula in PDF} with finitely many indecomposable components and with the property that See Formula in PDF \hbox{See Formula in PDF} and See Formula in PDF \hbox{See Formula in PDF} . We apply this corollary to give a short proof that locally quasiminimizing sets in the plane are BV_{l} extension domains.

Keywords: sets of finite perimeter, indecomposable sets

@article{COCV_2014__20_2_612_0, author = {Lorent, Andrew}, title = {On indecomposable sets with applications}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {612--631}, publisher = {EDP-Sciences}, volume = {20}, number = {2}, year = {2014}, doi = {10.1051/cocv/2013077}, mrnumber = {3264218}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2013077/} }

TY - JOUR AU - Lorent, Andrew TI - On indecomposable sets with applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 612 EP - 631 VL - 20 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2013077/ DO - 10.1051/cocv/2013077 LA - en ID - COCV_2014__20_2_612_0 ER -

%0 Journal Article %A Lorent, Andrew %T On indecomposable sets with applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 612-631 %V 20 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2013077/ %R 10.1051/cocv/2013077 %G en %F COCV_2014__20_2_612_0

Lorent, Andrew. On indecomposable sets with applications. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 2, pp. 612-631. doi : 10.1051/cocv/2013077. http://archive.numdam.org/articles/10.1051/cocv/2013077/

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