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Segment and corporate information (Details) - EUR (€)
€ in Thousands
 3 Months Ended 9 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2020
Sep. 30, 2019
Dec. 31, 2019
Segment and corporate information          
Revenue € 4,413,768 € 4,419,003 € 13,458,909 € 12,896,592  
Operating income 631,780 595,388 1,842,834 1,653,195  
Interest (87,692) (104,724) (283,851) (326,927)  
Income before income taxes 544,088 490,664 1,558,983 1,326,268  
Depreciation and amortization (396,179) (409,285) (1,200,726) (1,158,662)  
Impairment loss 3,154   (3,267)    
Income (loss) from equity method investees 24,173 20,544 48,487 63,058  
Total assets 33,049,135 33,169,403 33,049,135 33,169,403 € 32,934,735
thereof investments in equity method investees 706,994 682,617 706,994 682,617 € 696,872
Additions of property, plant and equipment, intangible assets and right of use assets 460,640 472,391 1,514,018 1,276,875  
Revenue from contracts with customers          
Segment and corporate information          
Revenue 4,317,276 4,323,175 13,153,165 12,617,501  
Other revenue          
Segment and corporate information          
Revenue 96,492 95,828 305,744 279,091  
Segment Total          
Segment and corporate information          
Revenue 4,405,352 4,413,231 13,427,813 12,881,260  
Operating income 721,763 678,268 2,131,162 1,895,048  
Depreciation and amortization (333,604) (348,476) (1,012,755) (982,468)  
Impairment loss 3,153   (3,234)    
Income (loss) from equity method investees 24,174 20,544 48,667 63,058  
Total assets 30,223,803 30,056,872 30,223,803 30,056,872  
thereof investments in equity method investees 706,994 682,617 706,994 682,617  
Additions of property, plant and equipment, intangible assets and right of use assets 386,947 382,527 1,216,101 1,033,446  
Segment Total | Revenue from contracts with customers          
Segment and corporate information          
Revenue 4,308,860 4,317,403 13,122,069 12,602,169  
Segment Total | Other revenue          
Segment and corporate information          
Revenue 96,492 95,828 305,744 279,091  
North America Segment          
Segment and corporate information          
Revenue 3,069,238 3,073,339 9,495,250 9,021,209  
Operating income 514,226 477,432 1,587,051 1,278,706  
Depreciation and amortization (244,800) (269,219) (758,967) (747,405)  
Impairment loss (389)   (993)    
Income (loss) from equity method investees 22,934 20,124 73,448 65,953  
Total assets 22,680,229 22,353,520 22,680,229 22,353,520  
thereof investments in equity method investees 394,756 385,604 394,756 385,604  
Additions of property, plant and equipment, intangible assets and right of use assets 285,348 286,472 891,954 777,523  
North America Segment | Revenue from contracts with customers          
Segment and corporate information          
Revenue 2,991,408 3,002,068 9,249,609 8,828,904  
North America Segment | Other revenue          
Segment and corporate information          
Revenue 77,830 71,271 245,641 192,305  
EMEA Segment          
Segment and corporate information          
Revenue 682,153 683,283 2,047,975 1,984,076  
Operating income 99,464 99,878 278,140 334,043  
Depreciation and amortization (47,073) (45,518) (141,824) (139,863)  
Impairment loss 3,542   (2,241)    
Income (loss) from equity method investees 1,114 (831) (23,441) (5,352)  
Total assets 3,855,469 4,056,993 3,855,469 4,056,993  
thereof investments in equity method investees 185,696 173,610 185,696 173,610  
Additions of property, plant and equipment, intangible assets and right of use assets 55,336 46,154 174,912 131,298  
EMEA Segment | Revenue from contracts with customers          
Segment and corporate information          
Revenue 674,704 676,340 2,026,561 1,951,464  
EMEA Segment | Other revenue          
Segment and corporate information          
Revenue 7,449 6,943 21,414 32,612  
Asia-Pacific Segment          
Segment and corporate information          
Revenue 483,897 474,551 1,377,003 1,360,123  
Operating income 96,892 90,382 237,012 254,441  
Depreciation and amortization (33,430) (24,709) (86,417) (70,139)  
Income (loss) from equity method investees 162 1,039 (1,273) 1,601  
Total assets 2,781,200 2,746,848 2,781,200 2,746,848  
thereof investments in equity method investees 100,466 98,863 100,466 98,863  
Additions of property, plant and equipment, intangible assets and right of use assets 32,528 37,789 104,801 83,707  
Asia-Pacific Segment | Revenue from contracts with customers          
Segment and corporate information          
Revenue 473,387 457,715 1,340,674 1,308,409  
Asia-Pacific Segment | Other revenue          
Segment and corporate information          
Revenue 10,510 16,836 36,329 51,714  
Latin America Segment          
Segment and corporate information          
Revenue 170,064 182,058 507,585 515,852  
Operating income 11,181 10,576 28,959 27,858  
Depreciation and amortization (8,301) (9,030) (25,547) (25,061)  
Income (loss) from equity method investees (36) 212 (67) 856  
Total assets 906,905 899,511 906,905 899,511  
thereof investments in equity method investees 26,075 24,540 26,075 24,540  
Additions of property, plant and equipment, intangible assets and right of use assets 13,735 12,112 44,434 40,918  
Latin America Segment | Revenue from contracts with customers          
Segment and corporate information          
Revenue 169,361 181,280 505,225 513,392  
Latin America Segment | Other revenue          
Segment and corporate information          
Revenue 703 778 2,360 2,460  
Corporate          
Segment and corporate information          
Revenue 8,416 5,772 31,096 15,332  
Operating income (89,983) (82,880) (288,328) (241,853)  
Depreciation and amortization (62,575) (60,809) (187,971) (176,194)  
Impairment loss 1   (33)    
Income (loss) from equity method investees (1)   (180)    
Total assets 2,825,332 3,112,531 2,825,332 3,112,531  
Additions of property, plant and equipment, intangible assets and right of use assets 73,693 89,864 297,917 243,429  
Corporate | Revenue from contracts with customers          
Segment and corporate information          
Revenue 8,416 5,772 31,096 15,332  
Operating Segments | Segment Total          
Segment and corporate information          
Revenue 4,415,642 4,414,100 13,454,921 12,883,642  
Operating Segments | North America Segment          
Segment and corporate information          
Revenue 3,077,455 3,074,058 9,517,490 9,022,903  
Operating Segments | EMEA Segment          
Segment and corporate information          
Revenue 683,984 683,304 2,052,383 1,984,097  
Operating Segments | Asia-Pacific Segment          
Segment and corporate information          
Revenue 484,081 474,586 1,377,215 1,360,614  
Operating Segments | Latin America Segment          
Segment and corporate information          
Revenue 170,122 182,152 507,833 516,028  
Operating Segments | Corporate          
Segment and corporate information          
Revenue (1,874) 4,903 3,988 12,950  
Inter-segment | Segment Total          
Segment and corporate information          
Revenue (10,290) (869) (27,108) (2,382)  
Inter-segment | North America Segment          
Segment and corporate information          
Revenue (8,217) (719) (22,240) (1,694)  
Inter-segment | EMEA Segment          
Segment and corporate information          
Revenue (1,831) (21) (4,408) (21)  
Inter-segment | Asia-Pacific Segment          
Segment and corporate information          
Revenue (184) (35) (212) (491)  
Inter-segment | Latin America Segment          
Segment and corporate information          
Revenue (58) (94) (248) (176)  
Inter-segment | Corporate          
Segment and corporate information          
Revenue € 10,290 € 869 € 27,108 € 2,382