{"gt_parse": {"text_sequence": ".If formula_73 is a E uclidean space and for mula_74 is the space of curve s in formula_9 (wi th the supremum dis tance formula_76 the n the length functional formula _77 which assi gns to eac h curve form ula_78 its len gth formula_ 79 is lower s emico ntinuous .Let for mula_8 0 be a me asure s pace and let formula_ 81 denote the set o f positive meas urable functions endowed with the topology of convergen ce in meas ure with resp ect t o formula_82 Then by Fat ou's lemm a th"}}