proposition: Lemma lebesgue_measure_ball (x r : R) : (0 <= r)%R -> lebesgue_measure (ball x r) = (r *+ 2)%:E.
proof: Proof. rewrite le_eqVlt => /predU1P[ <-|r0]. by rewrite (ball0 _ _).2// measure0 mul0rn. rewrite ball_itv lebesgue_measure_itv/= lte_fin ltrBlDr -addrA ltrDl. by rewrite addr_gt0 // -EFinD addrAC opprD opprK addrA subrr add0r -mulr2n. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop) reals ereal signed topology numfun normedtype HB(structures) sequences esum measure real_interval realfun exp lebesgue_stieltjes_measure