I guess the English translation for this would be either "Combat arena" or "Arena of warfare" (something along these lines).

My military dictionary gives this for מרחב לחימה :
מרחב שבו נערכות או מתוכננות להיערך פעולות צבאיות. גודלו של מרחב לחימה תלוי בגודל הכוחות שיפעלו בו וברמת המפקדה האחראית לפעולות בו, כגון: מרחב לחימה חטיבתי, אוגדתי וכיו"ב
The English translation it gives is "zone of operations".

I also found the following definitions for "battlespace":
Definitions:
(DOD) The environment, factors, and conditions that must be understood to successfully apply combat power, protect the force, or complete the mission. This includes the air, land, sea, space, and the included enemy and friendly forces; facilities; weather; terrain; the electromagnetic spectrum; and the information environment within the operational areas and areas of interest.
http://www.dtic.mil/doctrine/jel/doddict/data/b/9630.html

A unified military strategy to integrate and combine armed forces for the military theatre of operations, including air, information, land, sea and space to achieve military goals.
http://www.wordnik.com/words/battlespace

What nags me about these definitions is that the "space" in "battlespace" refers less to physical space (although it certainly includes it) - one definition refers mainly to environmental factors which include air etc the other refers to a military strategy..which includes air etc. That's why I thought זירה might be a more suitable substitute for מרחב as it is somewhat more....indirect/vague ...perhaps.


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Note added at 2 hrs (2011-12-18 23:14:39 GMT)
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In addition, although it may not be the same in Hebrew, in English, "arena" is perhaps a more suitable superordinate for air, land, sea, space, cyberspace, information etc...
Some of the definitions (including the ones I quoted) use "theatre of operations" ...although I think "arena" is an equally valid synonym.

www.proz.com/kudoz/english_to_german/military_defense/3190714-at_all_levels_of_the_battlespace.html

כאן נשאלה השאלה באנגלית לגרמנית.
התשובה שנבחרה פירושה שטחי העימות//איזורי העימות


combat area = שטח לחימה
combat zone = איזור-לחימה

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Note added at 2 hrs (2011-12-18 22:52:19 GMT)
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combat area = מרחב לחימה (כאמור

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Note added at 11 hrs (2011-12-19 08:11:11 GMT)
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אולי זירת קרב כשם משחק מחשב מפורסם

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Note added at 12 hrs (2011-12-19 08:59:43 GMT)
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Battlespace is a term used to signify a unified military strategy to integrate and combine armed forces for the military theatre of operations, including air, information, land, sea, and space to achieve military goals. It includes the environment, factors, and conditions that must be understood to successfully apply combat power, protect the force, or complete the mission. This includes enemy and friendly armed forces, infrastructure, weather, terrain, and the electromagnetic spectrum within the operational areas
and areas of interest.


לפי תיאור זה שנמצא בויקיפדיה מדובר בכלל באסטרטגיה צבאית
מאוחדת. צריך לבחור את התרגום בהתאם לקונטקסט הכללי

Merely another suggestion. I'm going a little further from the original in terms of terminology, but I think that my suggestion captures the gist of the original better than the others because
תנאים
unlike
מרחב/זירה
is more readily taken to mean everything from physical space to enemy forces to environment.

Hope this is helpful.